Question

Financial institutions often offer lower auto loan rates for new cars than used ones. A local credit union advertises new car loans at 2.79% APR and used car loans at 3.29% both for up to 72 months.

Tyresa wants to buy a car but doesn’t want to spend more than $350 a month for a maximum of four years. What is the maximum loan amount she can take out for a new car and a used car using the advertised rates?

Use the formula, A=P[(1+rn)nt−1]rn(1+rn)ntA=P1+rnnt-1rn1+rnnt where P is the monthly payment, r is the annual interest rate, n is the number times interest is compounded in one year, and t is the number of years. Show all of your steps.

Answer 1

When taking loan for a new car, the following are given:

P= $350, n=12*4 or, 48 and r=2.79% annual or, 2.79/(100*12) or, 0.002325 per month

Now the formuale for calulating the principal amount can be simplified and written as, P*(1-(1+r)^-n)/i

Putting the values we will get, =350*(1-(1+0.002325)^-48)/0.002325 or, 350*0.10548219/0.002325 or, $ 15879.04

If loan is taken on an used car, the r=3.29% or, 3.29/(100*12) or, 0.002741667, P= $350 and n=48

Putting the values in the above formulae we will get, =350*(1-(1+0.002741667)^-48)/0.002741667

or, 350*0.12315053/0.002741667 or, $ 15721.34

	Max Loan Amount
New Car	15879.04
Used Car	15721.34