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# Calculating the Return on Compounding Interest

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Suppose I deposit \$10,000 for 2 years at a rate of 10%.
how do I set up the problem and calculate the return (A) if the bank compounds annually (n = 1).?
Also I need to know to calculate the return (A) if the bank compounds quarterly (n = 4).? And Calculate the return (A) if the bank compounds monthly (n = 12)?

Please show me each calculation in order to get the answers also
calculate the return (A) if the bank compounds daily (n = 365)?
What observation can you make about the increase in mine return as my compounding increases more frequently?

if a bank compounds continuous, then I know the formula takes a simpler, that is
A=Pe^n
in a situation where e is a constant and equals approximately 2.7183.
How do I Calculate A with continuous compounding?
Now suppose, instead of knowing t, I know that the bank returned to me \$15,000 with the bank compounding continuously. Using logarithms, how do I find how long I left the money in the bank (find t)? , How long will it take to double my money? At 10% interest rate and continuous compounding please show me how you get your answer so I know how to figure it out?
I know 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=P(1+r/n)m

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.

#### Solution Preview

Hello!
We have first that P = \$10,000, r = 0.1 (10% expressed as decimal), t = 2 (2 years) n = 1.

The return A will then be:

A = 10000(1 + 0.1/1)^2 = \$10,201

When the bank compounds quarterly (n=4) we have to change two things. The most obvious one is that now n is 4 instead of 1. But another important change is that now we must NOT take (1+0.1/4) to the power of 2 as we did before. The value that goes in place of the 2 is the total number of compounding periods the bank gives you, which is t times n. In this case, n=4 and t=2, so t*n = 8. What does this 8 represent? It's just the number of quarters during which your bank compounded the return. Since you leave the deposit for 2 years, and each year has 4 quarters, then the deposit will grow over 8 quarters. The total return will now ...

#### Solution Summary

The return on continuing compounding interest is calculated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

\$2.19