Question

You've agreed on a deal for a new car. The purchase price is $25,000 of which you will finance $22,000 by taking out a loan from the dealer for 6.9% nominal interest compounded monthly for a term of 48 months. As you are about to sign the paperwork, you find that the dealer calculates your monthly payment to be $553.76/month.

(a).How much interest will you pay on this loan ($)?

(b). How much interest ($) SHOULD you be paying if the loan is actually at the stated principal, interest, and term?

(c).What is the nominal annual interest rate of the loan that the dealer based its calculation upon, assuming that the loan is actually based on a term of 48 months (percent, two decimal places)?

Answer 1

a)

Monthly payment amount=R=$553.76

Number of payments=n=48

Principal loan amount=PV=$22000

Total amount paid=553.76*48=$26580.48

Total interest paid=Total amount paid-Principal=26580.48-22000=$4580.48

b)

Interest rate per month=i=6.9%/12=0.575%

Monthly payment=PV/(P/A,0.575%,48)

Monthly payment=R=22000/41.84122=$525.80

Total amount paid=525.80*48=$25238.40

Total interest paid=Total amount paid-Principal=25238.40-22000=$3238.40

c)

We can Excel or financial calculators to get the interest rate in the given case. I would go for linear interpolation.

Let us see the value of PV factor at which monthly payment is 553.76.

(P/A,i,48)=PV/R=22000/553.76=39.7284

Let us calculate PV factor at i=8% (monthly 0.00667), 9% (monthly 0.0075), 10% (monthly 0.00833)

If we compare, we find that rate of interest should be between 9% and 10%

y1=40.18478

x1=9%

y2=39.42816

x2=10%

Linear interpolation can be done by using formula given below.

Let us find x for which y=39.7284

x=0.096032 or say 9.60%