Question

You deposit $5000 in a credit union at the end of each year for 10 years. The credit union pays 6% compound interest. Immediately after the tenth deposit, how much can withdraw from her account?

Answer 1

The objective is to find the future worth of n equal payments which are made at the end of every interest period till the end of the nth interest period at an interest rate of i compounded at the end of each interest period.

F = A[((1 + i)ⁿ – 1)/i]

F = A(F/A, i, n)

(F/A, i, n) = Equal payment series compound amount factor

A = Equal amount deposited at the end of each interest period

n = Number of interest periods

i = Interest rate

F = Single future amount

A = 5,000

n = 10 years

i = 6% or 0.06

F = 5,000[((1 + 0.06)¹⁰ – 1)/0.06]

F = 5,000(F/A, 6%, 10)

F = 5,000[((1.06)¹⁰ – 1)/0.06]

F = 5,000 × 13.181

F = $65,905.00

The future sum of the annual equal payments after 10 years is equal to $65,905.00