Borrower Brown borrowed $8,000 from the bank. He will pay 6% simple interest on the remaining balance of the loan in semi-annual equal PRINCIPAL payments for four years. How much total interest will Borrower Brown pay over the life of his loan?
I = PRT
I = 8,000 * 0.06 * 4
To calculate the total interest that Borrower Brown will pay over the life of his loan, we need to follow these steps:
Step 1: Determine the interest rate per period
The annual interest rate is 6%. Since the payments are made semi-annually, we need to divide the annual interest rate by the number of payment periods per year. In this case, there are two semi-annual payments, so the interest rate per period is 6% ÷ 2 = 3%.
Step 2: Determine the number of payment periods
The loan will be repaid over four years, and the payments are made semi-annually. Hence, the total number of payment periods will be 4 years × 2 = 8.
Step 3: Calculate the equal principal payment
To calculate the equal principal payment, we divide the loan amount by the total number of payment periods. In this case, the loan amount is $8,000, so the equal principal payment will be $8,000 ÷ 8 = $1,000.
Step 4: Calculate the interest for each payment period
To calculate the interest for each payment period, we multiply the remaining balance of the loan by the interest rate per period. Initially, the remaining balance is $8,000, so for the first payment period, the interest will be $8,000 × 3% = $240. After each payment, the remaining balance will be reduced, so we will calculate the interest for each subsequent period based on the new remaining balance.
Step 5: Calculate the total interest
To calculate the total interest, we add up the interest payments over all the payment periods. Since the interest payment is the same for each period, we can simply multiply the interest payment for one period by the total number of payment periods. In this case, the interest payment for one period is $240, and the total number of payment periods is 8. Therefore, the total interest paid will be $240 × 8 = $1,920.
Therefore, Borrower Brown will pay a total of $1,920 in interest over the life of his loan.