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All Textbook Solutions for Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Solve Problems 74-77 exactly without using a calculator. logxlog3=log4logx+4Solve Problems 74-77 exactly without using a calculator. ln2x2lnx1=lnxSolve Problems 74-77 exactly without using a calculator. lnx+3lnx=2ln2Solve Problems 74-77 exactly without using a calculator. log3x2=2+log9xWrite lny=5t+lnc in an exponential form free of logarithms. Then solve for y in terms of the remaining variables.Explain why 1 cannot be used as a logarithmic base.80REGiven Gx=0.3x2+1.2x6.9, find the following algebraically (to one decimal place) without the use of a graph: AInterceptsBVertexCMaximumorminimumDRangeGraph Gx=0.3x2+1.26.9 in a standard viewing window. Then find each of the following (to one decimal place) using appropriate commands. AInterceptsBVertexCMaximumorminimumDRangeElectricity rates. The table shows the electricity rates charged by Easton Utilities in the summer months. (A) Write a piecewise definition of the monthly charge Sx (in dollars) for a customer who uses xkWh in a summer month. (B) Graph Sx.Money growth. Provident Bank of Cincinnati, Ohio, offered a certificate of deposit that paid 1.25 compounded quarterly. If a 5,000 CD earns this rate for 5 years, how much will it be worth?Money growth. Capital One Bank of Glen Allen, Virginia, offered a certificate of deposit that paid 1.05 compounded daily. If a $5,000 CD earns this rate for 5 years, how much will it be worth?Money growth. How long will it take for money invested at 6.59 compounded monthly to triple?Money growth. How long will it take for money invested at 7.39 compounded continuously to double?Break-even analysis. The research department in a company that manufactures AM/FM clock radios established the following price-demand, cost, and revenue functions: px=501.25xPrice-demandfunctionCx=160+10xCostfunctionRx=xpx=x501.25xRevenuefunction where x is in thousands of units, and Cx and Rx are in thousands of dollars. All three functions have domain 1x40. (A) Graph the cost function and the revenue function simuta-neously in the same coordinate system. (B) Determine algebraically when R=C. Then, with the aid of part (A), determine when RCandRC to the nearest unit. (C) Determine algebraically the maximum revenue (to the nearest thousand dollars) and the output (to the nearest unit) that produces the maximum revenue. What is the wholesale price of the radio (to the nearest dollar) at this output?Profit-loss analysis. Use the cost and revenue functions from Problem 88. (A) Write a profit function and graph it in a graphing calculator. (B) Determine graphically when P=0,P0,andP0 to the nearest unit. (C) Determine graphically the maximum profit (to the near est thousand dollars) and the output (to the nearest unit) that produces the maximum profit. What is the wholesale price of the radio (to the nearest dollar) at this output? [Compare with Problem 88C.] (D) Use the models in parts (A) and (B) to find the equilibrium point. Write the equilibrium price to the nearest cent and the equilibrium quantity to the nearest unit.Construction. A construction company has 840 feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical rectangular storage areas sharing a common fence (see the figure). Assuming that all fencing is used, (A) Express the total area Ax enclosed by both pens as a function of x. (B) From physical considerations, what is the domain of the function A ? (C) Graph function A in a rectangular coordinate system. (D) Use the graph to discuss the number and approximate locations of values of x that would produce storage areas with a combined area of 25,000 square feet. (E) Approximate graphically (to the nearest foot) the values of x that would produce storage areas with a combined area of 25,000 square feet. (F) Determine algebraically the dimensions of the storage areas that have the maximum total combined area. What is the maximum area?Equilibrium point. A company is planning to introduce a 10-piece set of nonstick cookware. A marketing company established price-demand and price-supply tables for selected prices (Tables 1 and 2 ), where x is the number of cookware sets people are willing to buy and the company is willing to sell each month at a price of p dollars per set. (A) Find a quadratic regression model for the data in Table 1. Estimate the demand at a price level of $180. (B) Find a linear regression model for the data in Table 2. Estimate the supply at a price level of $180. (C) Does a price level of $180 represent a stable condition, or is the price likely to increase or decrease? Explain. (D) Use the models in parts (A) and (B) to find the equilibrium point. Write the equilibrium price to the nearest cent and the equilibrium quantity to the nearest unit.Crime statistics. According to data published by the FBI, the crime index in the United States has shown a downward trend since the early 1990sTable3. Find a cubic regression model for the crime index if x=0 represents 1987. Use the cubic regression model to predict the crime index in 2025.Medicine. One leukemic cell injected into a healthy mouse will divide into 2 cells in about 12 day. At the end of the day these 2 cells will divide into 4. This doubling continues until 1 billion cells are formed; then the animal dies with leukemic cells in every part of the body. (A) Write an equation that will give the number N of leukemic cells at the end of t days. (B) When, to the nearest day, will the mouse die?Marine biology. The intensity of light entering water is reduced according to the exponential equation I=I0ekd where I is the intensity d feet below the surface, I0 is the intensity at the surface, and k is the coefficient of extinction. Measurements in the Sargasso Sea have indicated that half of the surface light reaches a depth of 73.6 feet. Find k (to five decimal places), and find the depth (to the nearest foot) at which 1 of the surface light remains.Agriculture. The number of dairy cows on farms in the United States is shown in Table 4 for selected years since 1950. Let 1940 be year 0. (A) Find a logarithmic regression model y=a+blnx for the data. Estimate (to the nearest thousand) the number of dairy cows in 2023. (B) Explain why it is not a good idea to let 1950 be year 0.Population growth. The population of some countries has a relative growth rate of 3 (or more) per year. At this rate, how many years (to the nearest tenth of a year) will it takes a population to double?Medicare. The annual expenditures for Medicare (in billions of dollars) by the U.S. government for selected years since 1980 are shown in Table 5. Let x represent years since 1980. (A) Find an exponential regression model y=abx for the data. Estimate (to the nearest billion) the annual expenditures in 2025. (B) When will the annual expenditures exceed two trillion dollars?(A) Your sister has loaned you 1,000 with the understanding that you will repay the principal plus 4 simple interest when you can. How much would you owe her if you repaid the loan after 1 year? After 2 years? After 5 years? After 10 years? (B) How is the interest after 10 years related to the interest after 1 year? After 2 years? After 5 years? (C) Explain why your answers are consistent with the fact that for simple interest, the graph of future value as a function of time is a straight line (Fig. 1 ).Find die total amount due on a loan of $500 at 12 simple interest at the end of 30 months.Repeat Example 2 with a time period of 6 months.Repeat Example 3, assuming that you pay $9,828.74 for the T-bill.Repeat Example 4 assuming that 90 days after it was initially signed, the note was sold to a third party for $3,500.Repeat Example 5 if 500 shares of stock were purchased for $17.64 per share and sold 270 days later for $22.36 per share.A credit card has an annual interest rate of 16.99, and interest is calculated by the average daily balance method. In a 30 -day billing cycle, purchases of $345.86 and $246.71 were made on days 9 and 16, respectively, and a payment of 500.00 was credited to the account on day 15. If the unpaid balance at the start of the billing cycle was $1,792.19, how much interest will be charged at the end of the billing cycle? What will the unpaid balance be at the start of the next billing cycle?In Problems 1-4, if necessary, review Section A.I. If your stale sales tax rate is 5.65, how much tax will you pay on a bicycle that sells for 449.99 ?In Problems 1-4, if necessary, review Section A.I. If your state sales tax rate is 8.25, what is the total cost of a motor scooter that sells for 1,349.95 ?In Problems 1-4, if necessary, review Section A.I. A baseball team to had the a 10358 win-loss record Find its winning percentage to the nearest percentage point.In Problems 1-4, if necessary, review Section A.I . A basketball team played 21 games with a winning percentage of 81. How many games did it lose?In Problems 5-8, give the slope and y intercept of each line. (If necessary, review Section 1.2.) y=12,000+120xIn Problems 5-8, give the slope and y intercept of each line. (If necessary, review Section 1.2.) y=15,000+300xIn Problems 5-8, give the slope and y intercept of each line. (If necessary, review Section 1.2.) y=2,0001+0.025xIn Problems 5-8, give the slope and y intercept of each line. (If necessary, review Section 1.2.) y=5,0001+0.035xIn Problems 9-16.convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form. 6.210E11EIn Problems 9-16.convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal form. 4.3513E14E15E16EIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 180daysIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 9monthsIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 4monthsIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 90daysIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 5quartersIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 6weeksIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 40weeksIn Problems 17-24, convert the given time period to years, in reduced fraction form, assuming a 360 -day year [this assumption does not affect the number of quarters 4, months 12, or weeks 52 in a year ]. 7quartersIn Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. P=$300;r=7;t=2years;I=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. P=$950;r=9;t=1years;I=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=$36;r=4;t=6months;P=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=$15;r=8;t=3quarters;P=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=$48;P=$600;t=240days;r=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=$28;P=$700;t=13weeks;r=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=$60;P=$2,400;r=5;t=?In Problems 25-32, use formula 1 for simple interest to find each of the indicated quantities. I=96;P=3,200;r=4;t=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. P=4,500;r=10;t=1quarter;A=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. P=$3,000;r=4.5;t=30days;A=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$910;r=16;t=13weeks;P=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$6,608;r=24;t=3quarters;P=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$14,560;P=$13,000;t=4months;r=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$22,135;P=$19,000;t=39weeks;r=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$736;P=$640;r=15;t=?In Problems 33-40, use formula 2 for the amount to find each of the indicated quantities. A=$410;P=$400;r=10;t=?In Problems 41-46, solve each formula for the indicated variable. I=Prt;forrIn Problems 41-46, solve each formula for the indicated variable. I=Prt;forPIn Problems 41-46, solve each formula for the indicated variable. A=P+Prt;forPIn Problems 41-46, solve each formula for the indicated variable. A=P+Prt,forrIn Problems 41-46, solve each formula for the indicated variable. A=P1+rt;fortIn Problems 41-46, solve each formula for the indicated variable. I=Prt;fortDiscuss the similarities and differences in the graphs of future value A as a function of time t if $1.000 is invested at simple interest at rates of 4,8, and 12, respectively (see the figure).Discuss the similarities and differences in the graphs of future value A as a function of time t for loans of $400,$800. and $1,200, respectively, each at 7.5 simple interest (see the figure).In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If $3,000 is loaned for 4 months at a 4.5 annual rate, how much interest is earned?In all problems involving days,a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If $5,000 is loaned for 9 months at a 6.2 annual rate, how much interest is earned?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. How much interest will you have to pay for a 60 -day loan of $500, if a 36 annual rate is charged?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If a 50 annual rate is charged, how' much interest will be owed on a loan of $1.000 for 30 days?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. A loan of $7,260 was repaid at the end of 8 months. What size repayment check (principal and interest) was written, if an 8 annual rate of interest was charged?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. A loan of $10,000 was repaid at the end of 6 months. What amount (principal and interest) was repaid, if a 6.5 annual rate of interest was charged?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. A loan of $4,000 was repaid at the end of 10 months with a check for $4,270. What annual rate of interest was charged?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. A check for $3,097.50 was used to retire a 5 -month $3,000 loan. What annual rate of interest was charged?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If you paid $30 to a loan company for the use of $1,000 for 60 days, what annual rate of interest did they charge?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. If you paid $120 to a loan company for the use of $2,000 for 90 days, what annual rate of interest did they charge?A radio commercial for a loan company states: "You only pay 29c a day for each $500 borrowed.” If you borrow $1,500 for 120 days, what amount will you repay, and what annual interest rate is the company charging?George finds a company that charges 59c per day for each $1,000 borrowed. If he borrows $3,000 for 60 days, what amount will he repay, and what annual interest rate will he pay the company?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. What annual interest rate is earned by a 13 -week T-bill with a maturity value of $1,000 that sells for $989.37 ?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. What annual interest rate is earned by a 33 -day T-bill with a maturity value of $1,000 that sells for $996.16 ?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. What is the purchase price of a 50 -day T-bill with a maturity value of $1,000 that earns an annual interest rate of 5.53 ?In all problems involving days, a 360 -day year is assumed. When annual rates are requested as an answer, express, express the rate as a percentage, correct to three decimal places, unless directed otherwise. Round dollar amounts to the nearest cent. What is the purchase price of a 26 -week T-bill with a maturity value of $1,000 that earns an annual interest rate of 4.903 ?In Problems 65 and 66, assume that the minimum payment on a credit card is the greater of $20 or 2 of the unpaid balance. Find the minimum payment on an unpaid balance of $1,215.45.In Problems 65 and 66, assume that the minimum payment on a credit card is the greater of $20 or 2 of the unpaid balance. Find the minimum payment on an unpaid balance of $936.24.In Problems 67 and 68, assume that the minimum payment on a credit card is the greater of $27 or 3 of the unpaid balance. Find the minimum payment on an unpaid balance of $815.69.In Problems 67 and 68, assume that the minimum payment on a credit card is the greater of $27 or 3 of the unpaid balance. Find the minimum payment on an unpaid balance of $927.38.For services rendered, an attorney accepts a 90-day note for 5,500 at 8 simple interest from a client. (Both interest and principal are repaid at the end of 90 days.) Wishing to use her money sooner, the attorney sells the note to a third party for 5,560 after 30 days. What annual interest rate will the third party receive for the investment?To complete the sale of a house, the seller accepts a 180 -day note for $10,000 at 7 simple interest. (Both interest and principal are repaid at the end of 180 days.) Wishing to use the money sooner for the purchase of another house, the seller sells the note to a third party for $10,124 after 60 days. What annual interest rale will the third party receive for the investment?Use the commission schedule from Company A shown in Table 2 to find the annual rate of interest earned by each investment in Problems 71 and 72. An investor purchases 200 shares at 14.20 a share, holds the stock for 39 weeks, and then sells the stock for 15.75 a share.Use the commission schedule from Company A shown in Table 2 to find the annual rate of interest earned by each investment in Problems 71 and 72. An investor purchases 450 shares at 21.75 a share, holds the stock for 26 weeks, and then sells the stock for 24.60 a share.Use the commission schedule from Company B shown in Table 3 to find the annual rate of interest earned by each investment in Problems 73 and 74. An investor purchases 215 shares at 45.75 a share, holds the stock for 300 days, and then sells the stock for 51.90 a share.Use the commission schedule from Company B shown in Table 3 to find the annual rate of interest earned by each investment in Problems 73 and 74. An investor purchases 75 shares at 37.90 a share, holds the stock for 150 days, and then sells the stock for 41.20 a share.Many lax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is repaid when the IRS refund is sent to the firm. The RAL fee is equivalent to the interest charge for a loan. The schedule in Table 4 is from a major RAL lender. Use this schedule to find the annual rate of interest for the RALs in Problems 75-78. A client receives a 475 RAL, which is paid back in 20 days.Many lax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is repaid when the IRS refund is sent to the firm. The RAL fee is equivalent to the interest charge for a loan. The schedule in Table 4 is from a major RAL lender. Use this schedule to find the annual rate of interest for the RALs in Problems 75-78. A client receives a 1,100 RAL, which is paid back in 30 days.Many lax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is repaid when the IRS refund is sent to the firm. The RAL fee is equivalent to the interest charge for a loan. The schedule in Table 4 is from a major RAL lender. Use this schedule to find the annual rate of interest for the RALs in Problems 75-78. A client receives a 1,900 RAL, which is paid back in 15 days.Many lax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is repaid when the IRS refund is sent to the firm. The RAL fee is equivalent to the interest charge for a loan. The schedule in Table 4 is from a major RAL lender. Use this schedule to find the annual rate of interest for the RALs in Problems 75-78. A client receives a 3,000 RAL, which is paid back in 25 days.In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was 955.13.A5,000 purchase was made on the first day of the billing cycle and a 50 payment was credited to the account on day 21. How much interest will be charged at the end of the billing cycle?In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was 955.13.A50 payment was credited to the account on day 21 of the billing cycle and a 5,000 purchase was made on the last day of the billing cycle. How much interest will be charged at the end of the billing cycle?In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was 1,472.35. Purchases of 154.15 and 38.76 were made on days 5 and 12. respectively, and a payment of 250 was credited to the account on day 18. Find the unpaid balance at the end of the billing cycle.In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was 1,837.23. Purchases of 126.54 and 52.89 were made on days 21 and 27, respectively, and a payment of 100 was credited to the account on day 20. Find the unpaid balance at the end of the billing cycle.In Problems 83-86, assume that the annual interest rate on a credit card is 19.99 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30-day billing cycle was $654.71. No purchases were made during the billing cycle and a payment of $654.71 was credited to the account on day 21. Find the unpaid balance at the end of the billing cycle.In Problems 83-86, assume that the annual interest rate on a credit card is 19.99 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30-day billing cycle was $1,583.44. No purchases were made during the billing cycle and a payment of $1.583.44 was credited to the account on day 21. Find the unpaid balance at the end of the billing cycle.In Problems 83-86, assume that the annual interest rate on a credit card is 19.99 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30 -day billing cycle was. A purchase of $49.82 was made on day 15.No payment was made during the billing cycle and a late fee of $37 was charged to the account on day 25. Find the unpaid balance at the end of the billing cycle.In Problems 83-86, assume that the annual interest rate on a credit card is 19.99 and interest is calculated by the average daily balance method. The unpaid balance at the start of a 30-day billing cycle was $475.17. A purchase of $125.93 was made on day 3.No payment was made during the billing cycle and a late fee of $37 was charged to the account on day 25. Find the unpaid balance at the end of the billing cycle.A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Alabama, finance charges on a payday loan may not exceed 17.5 of the amount advanced. Find the annual interest rate if $500 is borrowed for 10 days at the maximum allowable charge.A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Illinois, charges on a payday loan may not exceed $15.50 per $100 borrowed. Find the annual interest rate if $400 is borrowed for 13 days at the maximum allowable charge.A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Kansas, charges on a payday loan may not exceed 15 of the amount advanced. Find the annual interest rate if 450 is borrowed for 7 days at the maximum allowable charge.A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. In Problems 87-90, express the annual interest rate as a percentage, rounded to the nearest integer. In Louisiana, charges on a payday loan may not exceed 16.75 of the amount advanced. Find the annual interest rate if 350 is borrowed for 14 days at the maximum allowable charge.Determine the value after 1 year of a 1,000 CD purchased from each of the banks in Table 1. Which CD offers the greatest return? Which offers the least return? If a principal P is invested at an annual rate r compounded m times a year, then the amount after 1 year is A=P1+rmm The simple interest rate that will produce the same amount A in 1 year is called the annual percentage yield APY. To find the APY, we proceed as follows: amountatsimpleinterestafter1year=amountatcompoundinterestafter1yearP1+APY=P1+rmmDividebothsidesbyP.1+APY=1+rmmIsolateAPYontheleftside.APY=1+rmm1 If interest is compounded continuously, then the amount after 1 year is A=Per. So to find the annual percentage yield, we solve the equation P1+APY=Per for APY, obtaining APY = er1. We summarize our results in Theorem 3(A) Which would be the better way to invest 1,000 : at 9 simple interest for 10 years, or at 7 compounded monthly for 10 years? (B) Explain why the graph of future value as a function of time is a straight line for simple interest, but for compound interest the graph curves upward (see Fig.1).Repeat Example 1 with an annual interest rate of 6 over an 8 -year period.What amount will an account have after 1.5 years if 8,000 is invested at an annual rate of 9 (A) compounded weekly? (B) compounded continuously? Compute answers to the nearest cent.How much should new parents invest at 8% to have 80,000 toward their child’s college education in 17 years if interest is Acompoundedsemiannually?Bcompoundedcontinuously?The Russell Index tracks the average performance of various groups of stocks. Figure 3 shows that, on average, a 10,000 investment in midcap growth funds over a 10 -year period would have grown to 63,000. What annual nominal rate would produce the same growth if interest were (A) compounded annually? (B) compounded continuously? Express answers as percentages, rounded to three decimal places.How long will it take 10,000 to grow to 25,000 if it is invested at 8 compounded quarterly?Southern Pacific Bank offered a 1 -year CD that paid 4.8 compounded daily and Washington Savings Bank offered one that paid 4.85 compounded quarterly. Find the APY (expressed as a percentage, correct to three decimal places) for each CD. Which has the higher return?What is the annual nominal rate compounded quarterly for a bond that has an APY of 5.8 ?In Problems 1-8, solve the equation for the unknown quantity. (If necessary, review sections A.7,2.5,and2.6.) 1,641.6=P1.23In Problems 1-8, solve the equation for the unknown quantity. (If necessary, review sections A.7,2.5,and2.6 ) 2.652.25=P1.032In Problems 1-8, solve the equation for the unknown quantity. (If necessary, review sections A.7,2.5,and2.6.) 12x3=58,956In Problems 1-8. solve the equation for the unknown quantity. (If necessary, review sections A. 7,2.5, and 2.6.) 100x4=15,006.25In Problems 1-8. solve the equation for the unknown quantity. (If necessary, review sections A. 7,2.5, and 2.6.) 6.75=31+i2In Problems 1-8. solve the equation for the unknown quantity. (If necessary, review sections A. 7,2.5, and 2.6.) 13.72=51+i3In Problems 1-8. solve the equation for the unknown quantity. (If necessary, review sections A. 7,2.5, and 2.6.) 14,641=10,0001.1nIn Problems 1-8. solve the equation for the unknown quantity. (If necessary, review sections A. 7,2.5, and 2.6.) 2,488.32=1,0001.2nIn Problems 9-12.use compound interest formula 1 to find each of the indicated values. P=$5,000;i=0.005;n=36;A=?In Problems 9-12.use compound interest formula 1 to find each of the indicated values. P=$2,800;i=0.003;n=24;A=?In Problems 9-12.use compound interest formula 1 to find each of the indicated values. A=$8,000;i=0.02;n=32;P=?In Problems 9-12.use compound interest formula 1 to find each of the indicated values. A=$15,000;i=0.01;n=28;P=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. P=$2,450;r=8.12;t=3years;A=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. P=$995;r=22;I=2years;A=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$6,300;r=9.45;t=8years;P=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$19,000:r=7.69;t=5years;P=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$88,000:P=71,153;r=8.5;t=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$32,982;P=$27,200;r=5.93;t=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$15,875:P=$12,100:t=48months;r=?In Problems 13-20.use the continuous compound interest formula 3 to find each of the indicated values. A=$23,600;P=$19,150;t=60months;r=?In Problems 2128, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 6.6 compounded quarterlyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 3.84 compounded monthlyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 5.52 compounded monthlyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 2.94 compounded semiannuallyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 7.3 compounded dailyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 5.44 compounded quarterlyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 4.86 compounded semiannuallyIn Problems 21-28, use the given annual interest rate r and the compounding to period to find i, the interest rate per compounding period. 10.95 compounded dailyIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 1.73 per half-yearIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 1.57 per quarterIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 0.53 per quarterIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 0.012 per dayIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 2.19 per quarterIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 3.69 per half-yearIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 0.008 per dayIn Problems 29-36, use the given interest rate i per compounding period to find r, the annual rale. 0.47 per monthIf $100 is invested at 6 compounded (A) annually (B) quarterly (C) monthly what is the amount after 4 years? How much interest is earned?If $2,000 is invested at 7 compounded AannuallyBquarterlyCmonthly what is the amount after 5 years? How much interest is earned?If $5,000 is invested at 5 compounded monthly, what is the amount after A2years?B4years?If $20,000 is invested at 4 compounded monthly, what is the amount after A5years?B8years?If $8,000 is invested at 7 compounded continuously, what is the amount after 6 years?If $23,000 is invested at 13.5 compounded continuously, what is the amount after 15 years?Discuss the similarities and the differences in the graphs of future value A as a function of time t if 1,000 is invested for 8 years and interest is compounded monthly at annual rates of 4,8,and12, respectively (see the figure).Discuss the similarities and differences in the graphs of future value A as a function of time t for loans of 4,000,8,000, and 12,000, respectively, each at 7.5 compounded monthly for 8 years (see the figure ).If $1,000 is invested in an account that earns 9.75 compounded annually for 6 years, find the interest earned during each year and the amount in the account at the end of each year. Organize your results in a table.If $2,000 is invested in an account that earns 8.25 com pounded annually for 5 years, find the interest earned during each year and the amount in the account at the end of each year. Organize your results in a table.If an investment company pays 6 compounded semiannually, how much should you deposit now to have 10,000 A5yearsfromnow?B10yearsfromnow?If an investment company pays 8 compounded quarterly, how much should you deposit now to have 6,000 A3yearsfromnow?B6yearsfromnow?If an investment earns 9 compounded continuously, how much should you deposit now to have $25,000 A36monthsfromnow?B9yearsfromnow?If an investment earns 12 compounded continuously, how much should you deposit now to have $4,800 A48monthsfromnow?B7yearsfromnow?What is the annual percentage yield (APY) for money invested at an annual rate of (A) 3.9 compounded monthly? (B) 2.3 compounded quarterly?What is the annual percentage yield (APY) for money invested at an annual rate of (A) 4.32 compounded monthly? (B) 4.31 compounded daily?What is the annual percentage yield (APY) for money invested at an annual rate of (A) 5.15 compounded continuously? (B) 5.20 compounded semiannually?What is the annual percentage yield ( APY ) for money invested at an annual rate of (A) 3.05 compounded quarterly? (B) 2.95 compounded continuously?How long will it take $4,000 to grow to $9,000 if it is invested at 1 compounded monthly?How long will it take $5,000 to grow to $7,000 if it is invested at 6 compounded quarterly?How long will it take $6,000 to grow to $8,600 if it is invested at 9.6 compounded continuously?How long will it take $42,000 to grow to $60,276 if it is invested at 4.25 compounded continuously?In Problems 59 and 60. use compound interest formula 1 to find n to the nearest larger integer value. A=2P;i=0.06;n=?In Problems 59 and 60. use compound interest formula 1 to find n to the nearest larger integer value. A=2P;i=0.05;n=?How long will it take money to double if it is invested at (A) 10 compounded quarterly? (B) 12 compounded quarterly?How long will it take money to double if it is invested at (A) 8 compounded semiannually? (B) 7 compounded semiannually?How long will it lake money to double if it is invested at (A) 9 compounded continuously? (B) 11 compounded continuously?How long will it take money to double if it is invested at (A) 21 compounded continuously? (B) 33 compounded continuously?A newborn child receives a $20,000 gift toward college from her grandparents. How much will the $20,000 be worth in 17 years if it is invested at 7 compounded quarterly?A person with $14,000 is trying to decide whether to purchase a car now, or to invest the money at 6.5 compounded semiannually and then buy a more expensive car. How much will be available for the purchase of a car at the end of 3 years?What will a $210,000 house cost 10 years from now if the inflation rate over that period averages 3 compounded annually?If the inflation rate averages 4 per year compounded annually for the next 5 years, what will a car that costs $17,000 now cost 5 years from now?Rental costs for office space have been going up at 4.8 per year compounded annually for the past 5 years. If office space rent is now $25 per square foot per month, what were the rental rates 5 years ago?In a suburb, housing costs have been increasing at 5.2 per year compounded annually for the past 8 years. A house worth $260,000 now would have had what value 8 years ago?(A) If an investment of $100 were made in 1776, and if it earned 3 compounded quarterly, how much would it be worth in 2026 ? (B) Discuss the effect of compounding interest monthly, daily, and continuously (rather than quarterly) on the $100 investment. (C) Use a graphing calculator to graph the growth of the investment of part (A).(A) Starting with formula 1, derive each of the following formulas: P=A1+in.i=AP1/n1,n=lnAlnPln1+i (B) Explain why it is unnecessary to memorize the formulas above for P,i, and n if you know formula 1.A promissory note will pay $50,000 at maturity 6 years from now. If you pay $28,000 for the note now, what rate compounded continuously would you earn?If you deposit $10,000 in a savings account now, what rate compounded continuously would be required for you to with draw $12,500 at the end of 4 years?You have saved $7,000 toward the purchase of a car costing $9,000. How long will the $7,000 have to be invested at 9 compounded monthly to grow to $9,000 ? (Round up to the next-higher month if not exact.)A married couple has $15,000 toward the purchase of a house. For the house that the couple wants to buy, a down payment of $20,000 is required. How long will the money have to be invested at 7 compounded quarterly to grow to $20,000 ? (Round up to the next-higher quarter if not exact.)An Individual Retirement Account (IRA) has $20,000 in it. and the owner decides not to add any more money to the account other than interest earned at 6 compounded daily. How much will be in the account 35 years from now when the owner reaches retirement age?If $1 had been placed in a bank account in the year 1066 and forgotten until now, how much would be in the account at the end of 2026 if the money earned 2 interest compounded annually? 2 simple interest? (Now you can see the power of compounding and why inactive accounts are closed after a relatively short period of time.)How long will it take money to double if it is invested at 7 compounded daily? 8.2 compounded continuously?How long will it take money to triple if it is invested at 5 compounded daily? 6 compounded continuously?In a conversation with a friend, you note that you have two real estate investments, one that has doubled in value in the past 9 years and another that has doubled in value in the past 12 years. Your friend says that the first investment has been growing at approximately 8 compounded annually and the second at 6 compounded annually. How did your friend make these estimates? The rule of 72 states that the annual compound rate of growth r of an investment that doubles in n years can be approximated by r=72/n. Construct a table comparing the exact rate of growth and the approximate rate provided by the rule of 72 for doubling times of n=6,7,,12 years. Round both rates to one decimal place.Refer to Problem 81. Show that the exact annual compound rate of growth of an investment that doubles in n years is given by r=10021/n1. Graph this equation and the rule of 72 on a graphing calculator for 5n20.Solve Problems 83-86 using graphical approximation techniques on a graphing calculator. How long does it lake for a $2,400 investment at 13 compounded quarterly to be worth more than a $3,000 investment at 6 compounded quarterly?Solve Problems 83-86 using graphical approximation techniques on a graphing calculator. How long does it lake for a $4,800 investment at 8 compounded quarterly to be worth more than a $5,000 investment at 5 compounded quarterly?Solve Problems 83-86 using graphical approximation techniques on a graphing calculator. One investment pays 10 simple interest and another pays 7 compounded annually. Which investment would you choose? Why?Solve Problems 83-86 using graphical approximation techniques on a graphing calculator. One investment pays 9 simple interest and another pays 6 compounded monthly. Which investment would you choose? Why?What is the annual nominal rate compounded daily for a bond that has an annual percentage yield of 3.39 ?What is the annual nominal rate compounded monthly for a bond that has an annual percentage yield of 2.95 ?What annual nominal rate compounded monthly has the same annual percentage yield as 7 compounded continuously?What annual nominal rate compounded continuously has the same annual percentage yield as 6 compounded monthly?Problems 91-94 refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures-no interest payments are made. A zero coupon bond with a face value of $30,000 matures in 15 years. What should the bond be sold for now if its rale of return is to be 4.348 compounded annually?Problems 9194 refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures-no interest payments are made. A zero coupon bond with a face value of $20,000 matures in 10 years. What should the bond be sold for now if its rate of return is to be 4.194 compounded annually?Problems 91-94 refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures-no interest payments are made. If you pay $4,126 for a 20 -year zero coupon bond with a face value of $10,000, what is your annual compound rate of return?Problems 91-94 refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures-no interest payments are made. If you pay $32,000 for a 5 -year zero coupon bond with a face value of $40,000. what is your annual compound rate of return?The buying and selling commission schedule shown in the table is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in Problems 95-98. An investor purchases 100 shares of stock at 65 per share, holds the stock for 5 years, and then sells the stock for 125 a share.The buying and selling commission schedule shown in the table is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in Problems 95-98. An investor purchases 300 shares of stock at $95 per share, holds the stock for 3 years, and then sells the stock for $156 a share.The buying and selling commission schedule shown in the table is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in Problems 95-98. An investor purchases 200 shares of stock at $28 per share, holds the stock for 4 years, and then sells the stock for $55 a share.The buying and selling commission schedule shown in the table is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in Problems 9598. An investor purchases 400 shares of stock at 48 per share, holds the stock for 6 years, and then sells the stock for 147 a share.(A) Discuss the similarities and differences in the graphs of future value FV as a function of time t for ordinary annuities in which $100 is deposited each month for 8 years and interest is compounded monthly at annual rates of 4,8, and 12, respectively (Fig. 3). (B) Discuss the connections between the graph of the equation y=100t, where t is time in months, and the graphs of part (A).Refer to Example 3 and Matched Problem 3. What was the total amount Jane deposited in order to have $143,785.10 at retirement? What was the total amount Mary deposited in order to have the same amount at retirement? Do you think it is advisable to start saving for retirement as early as possible?What is the value of an annuity at the end of 10 years if $1,000 is deposited every 6 months into an account earning 8 compounded semiannually? How much of this value is interest?A bond issue is approved for building a marina in a city. The city is required to make regular payments every 3 months into a sinking fund paying 5.4 compounded quarterly. At the end of 10 years, the bond obligation will be retired with a cost of $5,000,000. (A) What should each payment be? (B) How much interest is earned during the 10th year?Refer to Example 3. Mary starts a Roth IRA earning the same rate of interest at the time Jane stops making payments into her IRA. How much must Mary deposit each year for the next 25 years in order to have the same amount at retirement as Jane?A person makes annual deposits of $1,000 into an ordinary annuity. After 20 years, the annuity is worth $55,000. What annual compound rate has this annuity earned during this 20 -year period? Express the answer as a percentage, correct to two decimal places.In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) 1+2+4+8++29In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) 1+5+25+125++58In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) a=30,r=1,n=100In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) a=25,r=1,n=81In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) a=10,r=3,n=15In Problems 1-8, find the sum of the finite geometric series a+ar+ar2++arn1. (If necessary, review Section B.2.) a=4,r=10,n=6In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Quarterly deposits of $500 are made for 20 years into an annuity that pays 8 compounded quarterly.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Monthly deposits of $350 are made for 6 years into an annuity that pays 6 compounded monthly.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Semiannual deposits of 900 are made for 12 years into an annuity that pays 7.5 compounded semiannually.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Annual deposits of 2,500 are made for 15 years into an annuity that pays 6.25 compounded annually.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Monthly deposits of 235 arc made for 4 years into an annuity that pays 9 compounded monthly.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Semiannual deposits of $1,900 are made for 7 years into an annuity that pays 8.5 compounded semiannually.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Annual deposits of $3,100 are made for 12 years into an annuity that pays 5.95 compounded annually.In Problems 7-14, find i (the rate per period) and n (the number of periods )for each annuity. Quarterly deposits of 1,200 are made for 18 years into an annuity that pays 7.6 compounded quarterly.In Problems 15-22, use the future value formula 6 to find each of the indicated values. n=20:i=0.03;PMT=$500:FV=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. n=25:i=0.04;PMT=$100:FV=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$5,000;n=15;i=0.01;PMT=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$2,500;n=10;i=0.08;PMT=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$4,000;i=0.02;PMT=200;n=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$8,000;i=0.04;PMT=500;n=?In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$7,600;PMT=$500;n=10;i=? (Round answer to two decimal places.)In Problems 15-22, use the future value formula 6 to find each of the indicated values. FV=$4,100;PMT=$100;n=20;i=? (Round answer to two decimal places.)Explain what is meant by an ordinary annuity.Explain why no interest is credited to an ordinary annuity at the end of the first period.Solve the future value formula 6 for it.Solve the future value formula 6 for i if n=2.Guaranty Income Life offered an annuity that pays 6.65 compounded monthly. If $500 is deposited into this annuity every month, how much is in the account after 10 years? How much of this is interest?USG Annuity and Life offered an annuity that pays 7.25 compounded monthly. If $1,000 is deposited into this annuity every month, how much is in the account after 15 years? How much of this is interest?In order to accumulate enough money for a down payment on a house, a couple deposits $300 per month into an account paying 6 compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years?A self-employed person has a Keogh retirement plan. (This type of plan is free of taxes until money is withdrawn.) If deposits of $7,500 are made each year into an account paying 8 compounded annually, how much will be in the account after 20 years?Sun America offered an annuity that pays 6.35 compounded monthly. What equal monthly deposit should be made into this annuity in order to have $200,000 in 15 years?The Hartford offered an annuity that pays 5.5 compounded monthly. What equal monthly deposit should be made into this annuity in order to have $100,000 in 10 years?A company estimates that it will need $100,000 in 8 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 7.5 com pounded monthly, how much should each payment be?Parents have set up a sinking fund in order to have $120,000 in 15 years for their children's college education. How much should be paid semiannually into an account paying 6.8 compounded semiannually?If $1.000 is deposited at the end of each year for 5 years into an ordinary annuity earning 8.32 compounded annually, construct a balance sheet showing the interest earned during each year and the balance at the end of each year.If $2,000 is deposited at the end of each quarter for 2 years into an ordinary annuity earning 7.9 compounded quarterly, construct a balance sheet showing the interest earned during each quarter and the balance at the end of each quarter.Beginning in January, a person plans to deposit $100 at the end of each month into an account earning 6 compounded monthly. Each year taxes must be paid on the interest earned during that year. Find the interest earned during each year for the first 3 years.If $500 is deposited each quarter into an account paying 8 compounded quarterly for 3 years, find the interest earned during each of the 3 years.Bob makes his first $1,000 deposit into an IRA earning 6.4 compounded annually on his 24th birthday and his last $1,000 deposit on his 35th birthday ( 12 equal deposits in all). With no additional deposits, the money in the IRA continues to earn 6.4 interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob retires?Refer to Problem 39. John procrastinates and does not make his first $1,000 deposit into an IRA until he is 36. But then he continues to deposit $1,000 each year until he is 65 ( 30 deposits in all). If John's IRA also earns 6.4 compounded annually, how much is in his IRA when he makes his last deposit on his 65th birthday?Refer to Problems 39 and40. How much would John have to deposit each yearRefer to Problems 39 and 40. Suppose that Bob decides to continue to make $1.000 deposits into his IRA every year until his 65th birthday. If John still waits until he is 36 to start his IRA, how much must he deposit each year in order to have the same amount at age 65 as Bob has?Compubank, an online banking service, offered a money market account with an APY of 1.551. (A) If interest is compounded monthly, what is the equivalent annual nominal rate? (B) If you wish to have $10,000 in this account after 4 years, what equal deposit should you make each month?American Express's online banking division offered a money market account with an APY of 2.243. (A) If interest is compounded monthly, what is the equivalent annual nominal rate? (B) If a company wishes to have $1,000,000 in this account after 8 years, what equal deposit should be made each month?You can afford monthly deposits of $200 into an account that pays 5.7 compounded monthly. How long will it be until you have $7,000 ? (Round to the next-higher month if not exact.)A company establishes a sinking fund for upgrading office equipment with monthly payments of $2,000 into an account paying 6.6 compounded monthly. How' long will it be before the account has $100,000 ? (Round up to the next-higher month if not exact.)In Problems 47-50, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A person makes annual payments of $1,000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is $5,840. What annual nominal compounding rate has this annuity earned?In Problems 47-50, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A person invests $2,000 annually in an IRA. At the end of 6 years, the amount in the fund is $14,000. What annual nominal compounding rate has this fund earned?In Problems 47-50, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. An employee opens a credit union account and deposits $120 at the end of each month. After one year, the account contains $1,444.96. What annual nominal rate compounded monthly has the account earned?In Problems 47-50, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. An employee opens a credit union account and deposits $90 at the end of each month. After two years, the account contains $52,177.48. What annual nominal rate compounded monthly has the account earned?In Problems 51 and 52, use graphical approximation techniques to answer the questions. When would an ordinary annuity consisting of quarterly payments of $500 at 6 compounded quarterly be worth more than a principal of $5,000 invested at 4 simple interest?In Problems 51 and 52, use graphical approximation techniques to answer the questions. When would an ordinary annuity consisting of monthly payments of $200 at 5 compounded monthly be worth more than a principal of $10,000 invested at 7.5 compounded monthly?To purchase a home, a family plans to sign a mortgage of $70,000 at 8 on the unpaid balance. Discuss the advantages and disadvantages of a 20-year mortgage as opposed to a 30-year mortgage. Include a comparison of monthly payments and total interest paid.(A) A family has an $85,000, 30 -year mortgage at 9.6 compounded monthly. Show that the monthly payments are $720.94. (B) Explain why the equation y=720.9411.0081230x0.008 gives the unpaid balance of the loan after x years. (C) Find the unpaid balance after 5 years, after 10 years, and after 15 years. (D) When does the unpaid balance drop below half of the original $85,000 ? (E) Solve part (D) using graphical approximation techniques on a graphing calculator (see Fig. 3).How much should you deposit in an account paying 8 compounded quarterly in order to receive quarterly payments of $1,000 for the next 4 years?Refer to Example 2. If $2,000 is deposited annually for the first 25 years, how much can be withdrawn annually for the next 20 years?If you sell your car to someone for 2,400 and agree to finance it at 1 per month on the unpaid balance, how much should you receive each month to amortize the loan in 24 months? How much interest will you receive?Construct the amortization schedule for a $1,000 debt that is to be amortized in six equal monthly payments at 1.25 interest per monthA couple purchased a home 20 years ago for $65,000. The home was financed by paying 20 down and signing a 30-year mortgage at 8 on the unpaid balance. The net market value of the house is now $130,000, and the couple wishes to sell the house. How much equity (to the nearest dollar) does the couple have in the house now after making 240 monthly payments?Which option should you choose if your credit union raises its loan rate to 7.5 compounded monthly and all other data remain the same?The annual interest rate on a credit card is 24.99. How long will it take to pay off an unpaid balance of 1,485.73 if no new purchases are made and a 50.00 payment is made each month?In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B.2 ). 1+12+14+18++128In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B.2 ). 1+15+125+1125++157In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B. 2 ). 30+3+310+3100++31,000,000In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B.2 ). 10,000+1,000+100+10++110,000In Problems 1-6, find the sum of the finite geometric series a+ar+ar2++arn1. Write the answer as a quotient of integers. (If necessary, review Section B.2 ). 112+1418++128
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