Question

Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 6.0% APR. You monthly payments are $625 and you have just made your 24th monthly payment on your SUV.

a) What is the amount of your original loan?

The amount of the original loan is $ ------

b) Assuming that you have made all of the first 24 payments on time, what is the outstanding principal balance on your SUV loan?

After 24 payments, the outstanding principal balance on the loan is $ (round to the nearest dollar)

c) Assuming that you have made all of the first 24 payments on time, then how much interest have you paid over the first two years of your loan?

After 24 payments, the total amount of interest paid on the loan over the first two years is $ (round to the nearest dollar)

Answer 1

a) EMI = P * r * ( 1+r)n / [ ( 1+r)n - 1]

Here

EMI = monthly payment =$ 625

P = principal amount

r = monthly rate of interest = 6% / 12 = 0.5%

n = number of months to be paid = 60 months

625 = P * 0.5% * (1.005)60 / [ (1.005)60 - 1 ]

625 = P * 0.005 * 1.3488501525 / 0.3488501525

625 = P * 0.019332802

P = $ 32328.4755

Principal amount = $ 32,328.4755

b) Loan balance outstanding after 24 th payment made.

So, number of remaining payments = 60 - 24 = 36 payments.

EMI = P * r * ( 1+r)n / [ ( 1+r)n - 1]

Here

EMI = monthly payment =$ 625

P = Reuired principal amount

r = monthly rate of interest = 6% / 12 = 0.5%

n = number of months to be paid = 36 months

625 = P * 0.5% * (1.005)36 / [ (1.005)36 - 1 ]

625 = P * 0.005 * 1.1966805248 / 0.1966805248

625 = P * 0.030421937

P = $ 20,544.3851

Principal amount outstanding after 24th payment made = $ 20,544.3851

c) Calculation of the interest payment over first 24 payments.

Total amount paid over First 24 months including interest = $ 625 * 24 = $ 15,000

Principal amount paid over First 24 payment = Total principal amount( from a - Principal amount outstanding after 24th payment made( from b) = $ 32,328.4755 - $ 20,544.3851

Principal amount paid over First 24 payment = $ 11,784.0904

Interest amount paid over first 24 payment = Total amount paid over First 24 payment -Total principal amount paid over First 24 payment

= $ 15,000 - $ 11,784.0904

Interest amount paid over first 24 payment =$ 3,215.9096