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 compare those amounts to determine which option has the lower cost of credit.
Option 1:
The one-time payment at the end of a 5-year term means there are no monthly payments. We can use the formula for simple interest to find the total amount paid:
Total amount paid = Principal + Interest
Principal = $9,500
Interest = Principal * Rate * Time
= $9,500 * 0.07 * 5
= $3,325
Total amount paid = $9,500 + $3,325
= $12,825
Option 2:
The monthly payment is $166.57, and the loan term is 6 years. We can use the formula for compound interest to find the total amount paid:
Total amount paid = Monthly payment * Number of Payments
Number of Payments = 6 years * 12 months/year
= 72
Total amount paid = $166.57 * 72
= $11,999.04
Comparing the total amounts paid for each option:
Option 1: $12,825
Option 2: $11,999.04
Based on these calculations, option 2 has the lower cost of credit.