The formula for calculating the amount of money?

The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given by





A=P(1+r/n)^nt





A is the amount of the return.


P is the principal amount initially deposited.


r is the annual interest rate (expressed as a decimal).


n is the number of compound periods in one year.


t is the number of years.





Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.





Suppose you deposit $4,000 for 8 years at a rate of 7%.





a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.





Answer:





Show work in this space. Use ^ to indicate the power or use the Equation Editor in MS Word.





b) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.





Answer:





Show work in this space





c) Does compounding annually or monthly yield more interest? Explain why.





Answer:





Explain:








d) If a bank compounds continuously, then the formula used is


where e is a constant and equals approximately 2.7183.


Calculate A with continuous compounding. Round your answer to the hundredth's place.





Answer:





Show work in this space








e) A commonly asked question is, “How long will it take to double my money?” At 7% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.





Answer:





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The formula for calculating the amount of money?
(a) Substituting P = $4 000 and r = 0.07, n=1 and t = 8 into


A=P(1+r/n)^nt


gives


$4 000(1+0.07)^8 = $6872.74.





(b) Compounding monthly means there are n=12 compound periods in one year so this time we get


$4 000(1+0.07/12)^(8*12) = $4 000(1+0.00583)^96


= $6 991.31





(c) Compounding monthly gives more as you are earning interest on your interest on a more frequent basis.





(d) With continuous compounding the amount after 8 years is


$4 000e^(8*0.07) = $4 000*2.7183^(0.56)


= $7002.69





(e) Here we are being asked to find the time when A = 2P (our initial principal has doubled).


i.e. 2P = Pe^(0.07t)


Dividing through by P gives


2 = e^(0.07t)


and taking natural logarithms gives


ln(2) = 0.07t


so t= ln(2)/0.07


= 9.90 years.