Compound Interest

Question

you deposit $14,000

in an account that pays 5%

interest compounded quarterly.

A. Find the future value after one year.

B. Use the future value formula for simple interest to determine the effective annual yield.

Answer 1

Hi Travis,

A) Deposit Amount * (1 + i) ^ n

i = interest

n = # of compounding periods

14,000 * (1 + 5% / 4) ^ 4 = $14,713.23

Explanation: Annual interest rate is 5%, but since interest is compounded quarterly, we divide by 4 to get 1.25% a quarter. We raise to the power of 4 also because interest is compounded quarterly, and we need to find the value after one year; so 4 quarters. If interest was compounded on semi-annual basis, then we would raise to the power of 2, and we would divide 5% by 2.

B) (1 + Nominal Interest Rate / # of Compounding Periods) ^ # of Compounding Periods - 1

(1 + 5% / 4) ^ 4 - 1 = 5.09%

Please let me know if you have any additional questions.

Best,

Ahed A.