Question

Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 4.5%/year compounded monthly. If the future value of the annuity after 11 years is $55,000, what was the size of each payment?

Answer 1

The size of each payment was $322.78.

Step-by-step explanation:

This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = M * (((1 + r)^n - 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 11 years = $55,000

M = Monthly payment = ?

r = Monthly interest rate = 4.5% / 12 = 0.045 / 12 = 0.00375

n = number of months = 11 years * 12 = 132

Substituting the values into equation (1) and solve for M, we have:

$55,000 = M * (((1 + 0.00375)^132 - 1) / 0.00375)

$55,000 = M * 170.394706737074

M = $55,000 / 170.394706737074

M = $322.779979808101

Rounding to 2 decimal places, we have:

M = $322.78

Therefore, the size of each payment was $322.78.