Question

You plan to deposit $1,500 into an account at the end of the year for the next 10 years. If interest rates are 8 percent compounded daily. (Include time lines with your answer.)

1. How much will be in the account at the end of 10 years?
2. If the deposits are made at the beginning of the year rather than the end of the year, how much will be in the account at the end of 10 years?

Answer 1

Annual interest rate = 8.00%
Daily interest rate = 8.00% / 365
Daily interest rate = 0.021918%

Effective annual rate = (1 + Daily interest rate)^365 - 1
Effective annual rate = (1 + 0.00021918)^365 - 1
Effective annual rate = 1.08328 - 1
Effective annual rate = 0.08328 or 8.328%

Answer a.

Annual deposit = $1,500
Number of deposits = 10

Future value = $1,500 * 1.08328^9 + $1,500 * 1.08328^8 + ... + $1,500 * 1.08328 + $1,500
Future value = $1,500 * (1.08328^10 - 1) / 0.08328
Future value = $1,500 * 14.714166
Future value = $22,071.25

Answer b.

Annual deposit = $1,500
Number of deposits = 10

Future value = $1,500 * 1.08328^10 + $1,500 * 1.08328^9 + ... + $1,500 * 1.08328 + $1,500
Future value = $1,500 * 1.08328 * (1.08328^10 - 1) / 0.08328
Future value = $1,500 * 15.939562
Future value = $23,909.34