Question

You need to take a loan of $1,500. You have two repayment options:

- Option 1 : Short-term 6% interest loan with a term of 1 year

- Option 2 : 1-year simple interest amortized loan at 6% interest, monthly payments

Calculate the total interest paid for both plans. Explain why you pay more interest with one of the options, and which option you would prefer.

Answer 1

Answer:

Option 1:

Total Interest payment = 1500 * 6% = $90

Option 2:

Loan amount = P = $1,500

Monthly interest = R = 6%/12 = 0.5%

Number of months = N = 12

Monthly payment = P* R * (1 + R)^N / ((1 + R)^N - 1) = 1500 * 0.5% *(1 + 0.5%)^12 / ((1 + 0.5%)^12-1)

= $129.0996

= $129.10

Total interest payment = 129.10 * 12 - 1500 =$49.20

As such:

Interest payment under option 1 = $90

Interest payment under option 2 = $49.20

The interest payment under option 2 is lower since in monthly payment there is component of repayment which is reducing the outstanding balance over months resulting in reduction in interest payments over the months.

I would prefer option 2