Question

1. You would like to buy a Mazda Miata convertible for a purchase price of $27,500. You will take out a loan for the entire amount.

   1. You have excellent credit so you can secure a loan at 5% APR for 3 years. What is your monthly payment? How much will you pay in interest if you pay off the loan as scheduled?

   2. Now suppose instead you want to consider a 5 year loan at 6.5% APR. What is your monthly payment? How much will you pay in interest if you pay off the loan as scheduled?

   3. Compare the cost of the two loans.

Answer 1

1.Information provided:

Purchase price= present value= $27,500

Time= 3 years*12= 36 months

Monthly interest rate= 5%/12= 0.4167%

Enter the below in a financial calculator to compute the monthly payment:

PV= -27,500

N= 36

I/Y= 0.4167

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 824.20.

Hence, the monthly payment is $824.20.

Interest= ($824.20*36) - $27,500

= $29,671.20 - $27,500

= $2,171.20.

2.Information provided:

Purchase price= present value= $27,500

Time= 5 years*12= 60 months

Monthly interest rate= 6.5%/12= 0.5417%

Enter the below in a financial calculator to compute the monthly payment:

PV= -27,500

N= 60

I/Y= 0.5417

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 538.07.

Hence, the monthly payment is $538.07.

Interest= ($538.07.*60) - $27,500

= $32,284.20 - $27,500

= $4,784.20.

The 5 year loan at an interest rate of 6.5% costs more than the  3 year loan at an interest rate of 5% since you have to pay more towards interest.