Question

On September 1, 2018, Susan Chao bought a motorcycle for $34,000. She paid $1,100 down and financed the balance with a five-year loan at an annual percentage rate of 7.6 percent compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2018). Two years later, at the end of October 2020, Susan got a new job and decided to pay off the loan.

  

If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2020?

Answer 1

• First things first, the loan amount = cost -down payment
  • Loan amount = 34000-1100
  • Loan amount = 32900
• Next we find the monthly payment
  • We are given the following information

  • r	7.60%
    n	5
    frequency	12
    PV	$       32,900.00

  • We need to solve the following equation to arrive at the required PMT:
  • 
  • So the monthly PMT including interest and principal is 660.81
• Next we can create the amortization schedule thinking there was no prepayment:
  • 
  • Opening balance = previous year's closing balance
  • Closing balance = Opening balance-Principal repayment
  • PMT is calculated as per the above formula
  • Interest = 0.076 /12 x opening balance
  • Principal repayment = PMT - Interest

• So after 2 years or 24 payments, the closing balance was  $21,212.43 which was paid off by her
  • On this she was charged a 1% penalty so total she paid was:
  • $21,212.43 x 1.01 =  $21,424.55