Evaluate the following expression for P=2000, r = 9%, k = 2, and n= 12. P(1 + r/

Question

Evaluate the following expression for P=2000, r = 9%, k = 2, and n= 12. P(1 + r/K)kn P(1 + r/K)kn = (Do not round until the final answer. Then round to two decimal places as needed.) Suppose that $40,000 is invested at 7% interest. Find the amount of money in the account after 9 years if the interest is compounded annually. If interest is compounded annually, what is the amount of money after t = 9 years? dollars (Do not round until the final answer. Then round to the nearest cent as needed.) How much money will there be in an account at the end of 4 years if dollar 8000 is deposited at 6% interest compounded semi-annually? (Assume no withdrawals are made.) The amount after 4 years will be dollar . (Round to the nearest cent as needed.) An amount of dollar 4000 is invested at 12% interest, compounded daily. Find the future value in 7 years. Determine whether more or less money would have accrued if the money had been compounded quarterly. The total amount is dollar (Round to the nearest cent as needed.)

Explanation / Answer

1.) P = 2000 r= 9% n=2 k=12

P (1+r/n)nk = 2000 (1+ 9/200)24 = 2000 (1.045)24 = 5752.027668 = 5752.03

2.) P0 = $40000 r = 7% n=1 (annually) t = 9

final amount P = 40000 (1+ 7/100)9 = 73538.3685 = $ 73538.37

3.)  P0 = $8000    r = 6% n=2  (semi annually)    t =4

final amount P = 8000 (1+ 6/200)8 = 10134.16065 = $ 10134.16

4.a.) P0 = $4000    r = 12% n=365 (daily)    t =7

final P = 4000 (1+ 12/36500)2555 = 9264.188802 = $ 9264.19

b.) if n=4 Quarterly

final P = 4000 (1+ 12/400)28 = 9151.710703 = $ 9151.71 < $ 9264.19

less money will be procured if compounded Quarterly

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