Question

You plan to purchase a used motorcycle for $6,500. You can only afford a monthly payment of $200 for a period of two years. You can get a 9% loan, compounded monthly. Since you have lent money to your mother in the past, she has lovingly agreed to give you the down payment needed to get your monthly payment to the $200 level, if you promise that you will always wear a helmet. Ignoring the cost of the helmet, how much of a down payment must she provide?

Answer 1

Cost of Bike = $6,500
Monthly Payment = $200
Period of Loan = 2 years or 24 months
Annual Interest Rate = 9%
Monthly Interest Rate = 0.75% (9%/12)

Cost of Bike = Down Payment + Present Value of Monthly Payments
Down Payment = Cost of Bike - Present Value of Monthly Payments
Down Payment = $6,500 - $200 * PVIFA(0.75%, 24)
Down Payment = $6,500 - $200 * (1 - (1/1.0075)^24) / 0.0075
Down Payment = $6,500 - $200 * 21.88915
Down Payment = $2,122.17

So, she will provide a down payment of $2,122.17