Question

Sarafina is making monthly payments into an annuity. She wants to have $800 in fund to buy a new convection range in three months, and the account pays 7.2% annual interest. What are her monthly payments to the account?

To have $800 in the fund in three months, her monthly payments must be = $______

Answer 1

$265.07

Explanation:

The formula for the future value of an annuity is applicable.

A = P((1+r)^n-1)/r . . . . where r is the monthly interest rate and n is the number of months. P is the monthly payment, and A is the amount of the future value.

800 = P(1.006^3 -1)/(.006) = 3.018036P

P = 800/3.018036 ≈ 265.07

Sarafina's monthly payments need to be $265.07.

_____

This is about $1.60 less than the 266.67 she would deposit if she simply divided the desired balance by the number of months.

Because this number is rounded down, Sarafina will have a balance after 3 months of $799.99.