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.
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 answer