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.
To compare the two payment options, we need to find the total amount paid for each option and then calculate the cost of credit for each option.
Option 1:
Simple Interest = Principal x Rate x Time
Simple Interest = $9,500 x 0.07 x 5
Simple Interest = $3,325
Total amount paid = Principal + Interest
Total amount paid = $9,500 + $3,325
Total amount paid = $12,825
Cost of Credit = Total amount paid - Principal
Cost of Credit = $12,825 - $9,500
Cost of Credit = $3,325
Option 2:
We can use the compound interest formula to calculate the total amount paid.
Total amount paid = Monthly payment x Number of payments
Total amount paid = $166.57 x (12 payments/year) x 6 years
Total amount paid = $166.57 x 12 x 6
Total amount paid = $11,996.56
Cost of Credit = Total amount paid - Principal
Cost of Credit = $11,996.56 - $9,500
Cost of Credit = $2,496.56
Comparing the cost of credit for both options, we have:
Option 1: $3,325
Option 2: $2,496.56
The lower cost of credit is option 2, with a cost of credit of $2,496.56.