Answer: The United States rule is a method for calculating interest and balances on loans that have partial payments during their term. The rule assumes that each partial payment is applied to the interest first, then to the principal. Here's how to use the United States rule to calculate the balance and interest for this loan:
Calculate the daily interest rate by dividing the annual interest rate by 360 (the number of days in a standard year for most loans).
Daily Interest Rate = 15.0% / 360 = 0.04167%
Calculate the interest due for the first partial payment of $5800 made on day 112. Since this payment is larger than the remaining principal, it will pay off the loan entirely and no interest will accrue beyond this date.
- Days between start of loan and first payment = 112 days
- Interest due on first payment = (1450 x 0.04167% x 112) = $8.10
- Principal remaining after first payment = $0.00
Calculate the interest due for the second partial payment of $4350 made on day 196.
- Days between first payment and second payment = 84 days
- Interest due on second payment = (0 x 0.04167% x 84) = $0.00
- Principal remaining after second payment = $0.00
Calculate the interest due on the remaining principal at maturity (day 280).
- Days between second payment and maturity = 84 days
- Interest due at maturity = (0 x 0.04167% x 84) = $0.00
Add up the interest due from each period to get the total interest paid over the life of the loan.
- Total interest paid = $8.10 + $0.00 + $0.00 = $8.10
Add up the principal amounts from each payment to get the total amount paid.
- Total amount paid = $5800.00 + $4350.00 = $10,150.00
Subtract the total amount paid from the original principal to get the balance at maturity.
Balance at maturity = $1450.00 - $10,150.00 = -$8700.00 (which means the lender owes the borrower this amount)
Therefore, the balance at maturity is -$8700.00 (meaning the lender owes the borrower this amount) and the total interest paid over the life of the loan is $8.10.