There is a relationship between mortgage amount, number of payments, amount of each payment, how often eachpayment is made, and the interest rate. The following formula illustrates the relationship:PV=R[1-(1+i)"]i•PV = present value⚫ i = interest rate per compounding period, as a decimalR = payment amount• n = number of paymentsSuppose a bank offers you a 3.4% interest rate, compounded semi-annually, on a mortgage amount of $173 112.You pay $1000/mo, or $6000 semi-annually. How long, in years, would it take to pay off the mortgage?a. 80 yearsb. 60 yearsc. 20 yearsod. 40 yearse. 10 yearsAX

Step 1: Introduction to time value of moneyTime value of money is a financial concept which is used…

Answered: There is a relationship between…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The following equation gives the amount of money owed on a loan aftera certain amount of time if nt no payments are made. A P1+-) where: A= the amortized amount (total loan/investment amount over the life of the loan/investment) P=the initial amount of the loan/investment r= the annual rate of interest n-the number of times interest is compounded each year t 3 the time in years Find the amount owed at the end of 4 years if $2, 500 is loaned at a rate 4% compounded quarterly. %24 (Round answer to 2 decimal places. No dollar signs or commas.) Submit Question Search
Your parents just gave you $10,000 to be saved for a down payment on a home. You agree to save an additional $500 each month for the next three years in an investment account that compounds interest monthly. How much will you have saved at the end of three years assuming the annual interest rate is (a) 5% compounded monthly, (b) 7% compounded monthly, or (c) 9% compounded monthly? Formulas should include the =FV function and return a POSITIVE value. Initial investment Additional amount invested at the end of each month Term of investment (years) Compounding periods per year Interest rate 5% compounded monthly 7% compounded monthly 9% compounded monthly $10,000 $500 3 12 Future Value
Compute the specified quantity. The simple interest on a $3,000 loan at 6% per year amounted to $1080. At what time t did the loan mature (in years)? t = yr
Recall that the formula for earnings on a principal investment compounded annually is: A = P * (1 + r)t where: A = amount in the fund P = principal (initial amount invested) r = Annual Percentage Rate (APR) (as a decimal) t = time in years, or term If you invest $3,000 into each of the four options below, which option would yield the highest amount at the end of the term? a. 4 years, 10% APR b. 12 years, 3% APR c. 6 years, 7% APR d. 8 years, 5% APR
Find the compound amount and amount of deposit earned by the following deposit: $5600 at 3.5% compounded continuously for 9 years.
A building was bought for $130,000 and sold 17 years later for $470,000. What interest rate (compounded continuously) was earned on the investment? To find the interest rate earned on this investment, use the formula for continuous compound interest, where A is the final amount, P is the initial amount, r is the interest rate, and t is the time period. What is the formula for continuous compound interest? O A. A=Pe -rt B. A=P+ e rt OC. A=Pert rmt O D. A= 1+ Substitute the given values of A, P, and t into the formula. (Do not include the $ symbol in your answer.) What is the next logical step to solve this equation for r? A. Divide both sides of the equation by 130,000. O B. Divide both sides of the equation by 470,000. OC. Divide both sides of the equation by e(17).
Imagine that you currently have $10,000 in credit card debt. Suppose that your credit card charges 15% APR charged monthly. This means that your monthly interest rate r is given by the formula r=APR/12 If you make payments of $300 per month, how long would it take to pay off your credit card debt?
A person took out a loan of $100,000 from a bank thatcharges 7.5% interest compounded continuously. What should be the annual rate of payments if the loan is to be paid in full in exactly 10 years?
Many lending agencies compound interest more often than yearly, and as we noted in Example P.2, they are required to report the annual percentage rate, or APR, in a prominent place on the loan agreement. Furthermore, they are required to calculate the APR in a specific way. If r is the monthly interest rate, then the APR is calculated using APR = 12 ✕ r. (a) Suppose a credit card company charges a monthly interest rate of 1.8%. What APR must the company report? (Round your answer to the nearest tenth of a percent.) %(b) The phrase annual percentage rate leads some to believe that if you borrow $5000 from a credit card company which quotes an APR of 21.6%, and if no payments are made, then at the end of 1 year interest would be calculated at 21.6% simple interest on $5000. How much would you owe at the end of a year if interest is calculated in this way? (Round your answer to the nearest cent.)$ (c) If interest is compounded monthly (which is common), then the actual amount you would…
The equivalent present worth (P) of the cash flow in the accompanying diagram, where i =4% compounded annually is closest to:
If the balance, M, at time t in years, of a bank account that compounds its interest payments monthly is given by M = M0(1.07763)t(a) What is the effective annual rate for this account?(b) What is the nominal annual rate?
Use the compound interest formulas to a. calculate the total amount in the account after the given time period and b. determine the amount of interest earned. P= $5500, r 2.5% compounded weekly, t= 10 years P $4755, r 4.5% compounded monthly, t= 10 years P $7300, r 19.9% compounded continuously, t = 20 years

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