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 point)
Option
has the lower cost of credit, which is $
.
To compare the two payment options and determine which one has the lower cost of credit, we need to calculate the total amount paid for each option.
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
The total amount paid can be calculated using the formula: total amount = principal + (principal * interest rate * time)
In this case, the principal amount is $9,500, the interest rate is 7%, and the time is 5 years.
Total amount = $9,500 + ($9,500 * 0.07 * 5)
Total amount = $9,500 + ($9,500 * 0.35)
Total amount = $9,500 + $3,325
Total amount = $12,825
Option 2: Monthly payments of $166.57 with a fixed compound interest rate of 8% compounded monthly over a period of 6 years.
The total amount paid can be calculated using the formula: total amount = monthly payment * number of payments
In this case, the monthly payment is $166.57 and the number of payments is 6 years * 12 months = 72 payments.
Total amount = $166.57 * 72
Total amount = $11,995.04
Comparing the total amounts paid for each option, we find that option 2 has the lower cost of credit.
Option 2 has the lower cost of credit, which is $11,995.04.