Sly, the amount of money increases at a rate proportional to the amount S present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 8 years when $9000 is deposited in a savings account drawing 51% annual interest compounded continuously. (Round your answer to the nearest cent.) 4 $ 13698 (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years (c) Use a calculator to compare the amount obtained in part (a) with the amount S= 9000 1 + 9000(1 + (0.0525))** S = $ that is accrued when interest is compounded quarterly (Round your answer to the nearest cent.)
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- A certain some of money P draws interest compounded continuously. If a certain time there are Po dollars in the account, determine the time when the financial attains the value of 2Po dollars if the annual interest rate at 2%Suppose that $850,000 is invested in a savings account paying 5.25% interest per year. (Round answers to nearest hundredths or two decimal places.) a) Find the amount in the account after 11 years if interest is compounded monthly. 1 b) Find the amount in the account after 11 years if interest at continuous compound interest. c) How much interest was earned from continuous compounding in the 11 years? d) How long will it take for the amount in the account to grow to $2,000,000 if interest is compounded quarterly?The interest on a particular savings account is compounded continuously. The account initially had $2,200 deposited in it. The worth of the account after t-years can be calculated using the formula: A(t)=2200e0$1 (a) By what percent will the worth of the account increase per year? Round to the nearest hundredth of a percent. (b) To the nearest tenth of a year, how long will it take for the worth of the account to triple? (c) If another investment began with a principal of $2,500 and earned simplest interest of 3.8% applied once per year, which investment would be worth more after 10 years? Justify
- If you deposit $P into a savings account that earns interest at a rate of i% per month for n years, the future worth in year n is represented by all of the following equations, except: (a) F = $P(F∕P, effective i/month, 12n) (b) F = $P(F∕P, effective i/quarter, 3n) (c) F = $P(F∕P, effective i/6-month, 2n) (d) F = $P(F∕P, effective i/year, n)4. Suppose $5,000 is deposited in a savings and loan account that pays 5.5% interest compounded semiannually. Use compound interest to calculate the following:a. How much money will be saved?b. How much will be owed after 2 years?2. Suppose $2000 is deposited in a saving account that pays interest at an annual rate of 0.40%, compounded continuously. In addition, $100 is deposited into the account each year. What is the total amount of the money after 10 years? (Round off your answer to 2 decimal places.)
- The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $9000 in three years? a Click the icon to view some finance formulas. ..... The amount of money that should be deposited is $ (Round up to the nearest cent.) Formulas In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form. nt A A = P 1+ P = A =Pet Y = - 1 nt 1+ Print DoneSuppose you invest S11.570.00 into an account earming an interest rate of 2.484% compounded continuously for 2 yeart and thereafter earning an interest rate of 3.417% compounded weekly. How much money is in the account after 9 years? The amount in the account is (Note: Your answer should have a dollar sign and be accurate to two decimal places)
- 3. DETAILS ZILLDIFFEQMODAP11 3.1.010. (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years Need Help? When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 7 years when $3000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer to the nearest cent.) $ (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 3000 1 + S = $ Read It 7(4) 3000(1+1(0.0575)) (*) MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)Compounding The APY of a savings account is the percentage increasein the balance over the course of a year. Suppose you deposit $500 in a savings account that has an APY of 6.18% per year. Assume the interest rate remains constant and no additional deposits or withdrawals are made. How long will it take the balance to reach $2500?The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Click the icon to view some finance formulas. A. Find how much money there will be in the account after the given number of years. B. Find the interest earned. A. The amount of money in the account after 2 years is $. (Round to the nearest hundredth as needed.) Principal $7000 B. The amount of interest earned is $ (Round to the nearest hundredth as needed.) Rate 7% Compounded quarterly Time 2 years