An 8% interest loan with payments of $299.17 had a balance of $8,550 after the July 1st payment. The borrower paid the regular scheduled payment on August 1st, then immediately paid the entire remaining balance. If a 3% prepayment penalty was imposed, how much was the borrower charged for the prepayment penalty? (Interest paid in arrears)
To find out how much the borrower was charged for the prepayment penalty, we'll need to determine the remaining balance of the loan after the August 1st payment, including any interest accrued.
First, let's calculate the interest for the July 1st payment. Since the interest is paid in arrears, the interest for that payment covers the period from June 1st to June 30th.
Interest = Loan balance * Interest rate
Interest = $8,550 * 8% = $684
Now, let's calculate the remaining balance after the July 1st payment:
Remaining balance = Loan balance + Interest - Payment
Remaining balance = $8,550 + $684 - $299.17 = $8,934.83
For the August 1st payment, the borrower made the regular scheduled payment of $299.17. Let's calculate the interest for this payment, which covers the period from July 1st to July 31st.
Interest = Remaining balance * Interest rate
Interest = $8,934.83 * 8% = $714.79
Now, let's calculate the new remaining balance after the August 1st payment:
Remaining balance = Remaining balance + Interest - Payment
Remaining balance = $8,934.83 + $714.79 - $299.17 = $9,350.45
Since the borrower immediately paid the entire remaining balance after the August 1st payment, we'll apply the prepayment penalty of 3% to the remaining balance amount.
Prepayment penalty = Remaining balance * Prepayment penalty rate
Prepayment penalty = $9,350.45 * 3% = $280.51
Therefore, the borrower was charged a prepayment penalty of $280.51.