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 determine the lower cost of credit, we need to calculate the total amount paid for each payment option.
For Option 1:
The simple interest formula is: Interest = Principal x Rate x Time
Interest = $9,500 x 0.07 x 5 = $3,325
Total amount paid = Principal + Interest = $9,500 + $3,325 = $12,825
For Option 2:
The compound interest formula is: A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.
Using this formula, we can calculate the final amount for the monthly payments.
A = $166.57(1 + 0.08/12)^(12*6) = $166.57(1.00666667)^(72) = $166.57(1.63984351) = $273.09
Total amount paid = Monthly payment x Number of months = $166.57 x 12 x 6 = $11,993.44
Therefore, the lower cost of credit is Option 2 with a total amount paid of $11,993.44.