Question

A young graduate is planning on saving $686.00 each quarter for four years in an investment account paying 14.68% interest that is compounded quarterly. His first deposit will be made at the end of the next quarter, so this is a regular annuity. The balance from this investment account will be used as a down payment on a new car. Also, in 4 years, he also plans on being able to afford a 60-month car loan with $360.00 monthly payments at a 12.84% APR interest rate. Given the graduate’s plans, how expensive of a “dream car” will he expect to be able to purchase in four years?

Answer 1

Solution

First the future value of annuity of 686 will be calculated

Future value of annuity=Annuity amount*(((1+r)^n-1)/r)

Where

n=number of periods=4*4=16

r=intrest rate per period=14.68/4=3.67%

Annuity amount=686

Future value of annuity=686*(((1+.0367)^16-1)/.0367)

=14582.1023 (This will be used as the downpayment for the car)

Vow the prersent value of the loan payments will be calculated

Present value of annuity=Annuity payment*((1-(1/(1+i)^m))/i)

Where

i=intrest rate per period= 12.84%/12=1.07%

m=number of periods=60

Annuity payment=360

Present value of annuity=360*((1-(1/(1+.0107)^60))/.0107)

Present value of annuity=15879.14112=Present value of loan payment

Thus the amount for which he can purchase a car=Downpayment amount of car+Present value of loan payment

=14582.1023+15879.14112

Thus the amount for which he can purchase a car=30461.24342