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 6.3% APR. You monthly payments are $640 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 $. (round to the nearest dollar)

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

Sol:

APR (r) = 6.3%, Monthly = 6.3%/12 = 0.525%

PMT = $640

Period (nper) = 60

Original loan amount (PV)

a) Original loan amount will be: (In excel)

=PV(rate,nper,pmt)

=PV (0.525%,60,640,0)

PV = $32,866.69 or $32,867

The amount of the original loan is $32,867

b) APR (r) = 6.3%, Monthly = 6.3%/12 = 0.525%

PMT = $640

Period (nper) = 60, Remaining nper = 60 - 24 = 36

Original loan amount (PV)

Outstanding principal balance on your SUV loan after 24 payments will be: (In excel)

=PV(rate,nper,pmt)

=PV (0.525%,36,640,0)

PV = $20,943.74 or $20,944

After 24 payments, the outstanding principal balance on the loan is $20,944

c) Original PV = $32,867

APR (r) = 6.3%, Monthly = 6.3%/12 = 0.525%

Period (n) = 24 months

Interest you have paid over the first two years of your loan will be:

Future value (FV) = PV x (1+r)^n

Future value (FV) = $32,867 x (1+0.525%)^24

Future value (FV) = $32,867 x (1.00525)^24 = $37,268.17

FV after 2 years will be $37,268

Interest paid = FV - PV

Interest paid = $37,268 - $32,867 = $4401

After 24 payments, the total amount of interest paid on the loan over the first two years is $4401