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 $
Option 1: One-time payment at the end of a 5-year term with a simple interest rate of 7%.
To calculate the total cost of credit for Option 1, we can use the formula:
Total cost of credit = Principal + Interest
The principal is the original amount borrowed, which is $9,500.
The interest can be calculated using the formula:
Interest = Principal * Rate * Time
Where the rate is the interest rate and the time is the number of years.
Interest = $9,500 * 0.07 * 5 = $3,325
Total cost of credit = $9,500 + $3,325 = $12,825
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.
To calculate the total cost of credit for Option 2, we need to calculate the total amount paid over the 6-year period. Since the payments are made monthly, there will be a total of 6*12 = 72 payments.
Total amount paid = Monthly payment * Number of payments
Total amount paid = $166.57 * 72 = $11,998.04
Total cost of credit = Total amount paid - Principal
Total cost of credit = $11,998.04 - $9,500 = $2,498.04
Comparing the two options, Option 2 has the lower cost of credit, which is $2,498.04.