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 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.