Compounding: Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest-on-interest after six years?

Question

Quizplus · Accepted Answer

The formula for compound interest is:

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

Where:

A = the amount of money accumulated after n years,
P = the principal (the initial amount of money),
r = the annual interest rate (as a decimal),
n = the number of times the interest is compounded per year, and
t = the number of years.

In this case, P = $17,500, r = 0.0825 (8.25% expressed as a decimal), n = 12 (monthly compounding), and t = 6.

So, A = $17,500(1 + 0.0825/12)^(12*6)
A = $17,500(1.006875)^72
A = $31,997.63

The interest earned is $31,997.63 - $17,500 = $14,497.63.

The interest-on-interest, also known as compound interest on the interest earned, is the difference between the total amount earned and the principal. So, the interest-on-interest is $31,997.63 - $17,500 - $14,497.63, which is equal to $2,497.63.

Therefore, the answer is C, $2,497.63.

Compounding: Dat Nguyen Is Depositing $17,500 in an Account Paying