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# calculating of couponding interest

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The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by
A is the amount of returned.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the compound period.
t is the number of years.

Carry all calculations to 6 decimals on all assignments then round the answer to the nearest cent.

Suppose you deposit \$10,000 for 2 years at a rate of 10%.
a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the hundredth's place.
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b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
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c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
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d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
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e) What observation can you make about the size of the increase in your return as your compounding increases more frequently?

f) If a bank compounds continuously, then the formula takes a simpler, that is

where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.

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g) Now suppose, instead of knowing t, we know that the bank returned to us \$15,000 with the bank compounding continuously. Using natural logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.
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h) A commonly asked question is, "How long will it take to double my money?" At 10% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
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https://brainmass.com/math/fractions-and-percentages/calculating-of-couponding-interest-107915

#### Solution Preview

Please see the attached file for detailed solution.

e) The return ...

#### Solution Summary

The solution is comprised of detailed explanations of the calculation of the compounding interest. It also includes the application of logarithm.

\$2.19