Suppose youve bought a car worth 30000 and plan to pay it of

Suppose you’ve bought a car worth $30,000, and plan to pay it off over 60 monthly payments. However, you are given a 3 month grace period during which interest is still earned (skip 3 payments) before your monthly payments begin. What will be the monthly payments if your nominal interest rate is 6% compounded monthly?

Solution

ANSWER:

PV = $30,000

i = 6% per year or 6% / 12 per month or 0.5% per month

n = 60 months

since there is a 3 months grace period, we will find out the future value of this present value at the end of the 3 months.

fv = pv(f/p,i,n)

fv = 30,000(f/p,0.5%,3) = 30,000 * 1.015 = $30,450

now this future value will be treated as the present value after 3 months with interest rate of 0.5% per month and the no of periods as 57.

amount = pv(a/p,i,n) = 30,450(a/p,0.5%,57 = 30,450 * 0.0202 = $615.27

hence i need to pay $615.27 per month.