Compare the two payment options for a $9,500 loan to determine which option has the lower cost of credit.

Option 1: One-time payment to pay off the loan at the end of a 5-year term with a simple interest rate of 7%.

Option 2: Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly; payments made monthly over a period of 6 years.
Find the lower cost of credit. Round the answer to two decimal places as needed.

1 answer

To compare the two payment options, we first need to calculate the total cost of each option, including the principal and the interest.

Option 1: One-time payment at the end of 5 years with a simple interest rate of 7%.
The simple interest formula is: Interest = Principal x Rate x Time
Interest = $9,500 x 0.07 x 5 = $3,325
Total cost = Principal + Interest = $9,500 + $3,325 = $12,825

Option 2: Monthly payment of $166.57 with a fixed compound interest rate of 8% compounded monthly.

First, we need to calculate the total number of payments over 6 years:
Total number of payments = 6 years x 12 months/year = 72 payments

Next, we calculate the future value of the loan using the compound interest formula:
Future Value = Principal x (1 + Rate/Compounding frequency)^(Compounding frequency x Time)
Future Value = $166.57 x (1 + 0.08/12)^(12 x 6) = $12,301.41

Total cost = Total number of payments x Monthly payment amount = 72 x $166.57 = $11,997.04

Therefore, the option with the lower cost of credit is Option 2, with a total cost of $11,997.04.