Question

On September 1, 2013, Susan Chao bought a motorcycle for $23,000. She paid $1,200 down and financed the balance with a five-year loan at an APR of 6.5 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2013). Two years later, at the end of October 2015, Susan got a new job and decided to pay off the loan.

If the bank charges her a 2 percent prepayment penalty based on the loan balance. how much must she pay the bank on Nov. 1st 2015?

Answer 1

The loan amount is $23,000 - $1,200 = $21,800.

Monthly rate is (6.5% / 12) = 0.54167%.

The monthly payment is calculated below:

(1-(1+i) - Loan amount = Monthly payment x

21,800 = Monthly payment x 1-(1+0.0054167)-60 0.0054167

21,800 = Monthly payment x 51.11

426.54 = Monthly payment

Loan outstanding on Nov 1st 2015 is calculated below:

Loan amount = 426.54 x 1- (1 + 0.0054167)-35 1-1.0054167-1

Loan amount = 13,639.25

The amount payable on Nov 1st 2015 is $13,639.25 × 1.02 = $13,912.04.