Question

A man wants to buy a new car that has a cash price of $20,000. He makes a down payment of $2,000, and will have payments of $360 that are paid once a month for 5 full years.

1. What is the approximate APR for this car? (7.9% , 5.0% , or 3.5%)

2. How much is the total finance charge the man will end up paying for this car? ($3,600 , $6,320 , or $1,600)

Answer 1

1) Here EMI = $360

r = rate of interest = ?

Loan amount = Cash price - down payment

= 20000-2000

=$18000

n = no of installment = 5 x 12 = 60

Now, EMI = Loan amount/PVIFA(r%,n)

Thus, 360 = 18000/PVIFA(r%,60)

PVIFA(r%,60) = 18000/360

PVIFA(r%,60) = 50

Now assume r = 7.9%

Thus for PVIFA(r%,60) , r = 7.9%/12 = 0.6583%

Thus PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(0.6583%,60) = [1-(1/(1+0.6583%)^60 / 0.6583%]
=[1-(1/(1+0.006583)^60 / 0.006583]
=[1-(1/(1.006583)^60 / 0.006583]
=[1-0.6746 / 0.006583]
=0.3254/0.006583
=49.44

Thus approximately r = APR = 7.9%

2) Total Amount to be paid over life of loan = EMI x No of months

= 360 x 60

= 21600 $

Thus Interest paid over life of loan = Total Amount to be paid over life of loan - Loan amount

= $21600 - $18000

= $ 3,600