Question

A total of $54,000 is borrowed and repaid with 48 monthly payments, with the first payment occurring one month after receipt of the $54,000. The stated interest rate is 8.50% compounded quarterly. What monthly payment is required

Answer 1

Answer: $1,329.40

Step-by-step explanation:

First convert the annual interest rate which is compounded quarterly to an effective rate per period.

effective rate = (1 + annual rate/ no of compounding periods) ^ (number of compounding periods/ no. of periods) - 1

= (1 + 8.5%/4) ⁴ ⁺ ¹² - 1

= 0.703%

The monthly payments are constant so this is an Annuity.

Present value of Annuity = Annuity * (1 - ( 1 + r) ^ -n) / r

54,000 = Annuity * ( 1 - (1 + 0.703%)⁻⁴⁸) / 0.703%

54,000 = Annuity * 40.6205

Annuity = 54,000 / 40.62

Annuity = $1,329.40