Calculating Early Loan Repayments

Let's assume that you've come into a nice sum of money and decided to repay a loan before its scheduled due date. The early repayment should reduce your total financing costs because the lender will have its money returned to it ahead of schedule. But, you may be required to compensate the lender, who stands to lose interest income because of the early retirement of the loan. Any potential penalties and rebates in financing costs from prepayment should be addressed in the contract that you signed when the loan was first made. Some agreements permit you to prepay without a penalty; others may not.

For example, if you've borrowed $9,000 for twenty-four months, with the full principal and interest to be repaid in one single payment at the end of that time, but you instead decided to repay the loan after twelve months, you'll be charged only half of the scheduled interest charges. That's simple enough to understand. But, the amount required for early repayment of an installment loan is somewhat more difficult to compute than that for a single-payment loan, because installment loans involve a series of equal payments that are allocated partly to principal reduction and partly to interest. When an installment loan is repaid early, the lender must determine the amount of the remaining payments that represent interest charges to be deducted in calculating the payoff. In other words, if you intend to pay off a loan that has fifteen payments remaining of $500 each, you shouldn't be required to repay $5,000 ($500 x 10), because a significant portion of those payments represent interest that should not be charged.

Lenders frequently use the rule of 78s to determine the amount that must be paid by a borrower who wishes to repay an installment loan ahead of schedule. The technique calculates the interest portion of all the remaining installment payments. Here's how it works:

We'll assume this time that you borrowed $10,000, but you signed a loan agreement that calls for 24 monthly payments of $500 each. The interest charges over the life of the loan are equal to the total of all your scheduled payments ($12,000) minus the principal amount that you borrowed ($10,000), or $2,000. Let's say that after eighteen months you decide that you're going to pay off the remaining balance of the loan.

According to the rule of 78s, the lender will calculate your required payoff amount by determining the sum of the digits for all the scheduled payments (i.e., 24 + 23 + 22 + ... +1, which equals 300) and the sum of the digits for the remaining payments (i.e., 6 + 5 + 4 + 3 + 2 +1, which equals 21). The sum of the digits for the remaining payments (21) is divided by the sum of the digits of the entire loan (300). This fraction is then multiplied by the total interest charges ($2,000) to determine the scheduled interest that you should not have to pay due to the loan's early retirement. The reduction in interest is then subtracted from the sum of all of the remaining payments to determine the amount that you'll need in order to pay off the debt. The calculations are as follows:


sum of digits of remaining payments/sum of digits of all payments = 21/300 = .070

The scheduled interest (which you should not pay) that's included in the last 6 payments is equal to the fraction calculated above multiplied by the loan's total scheduled interest charges, or


.070 x $2,000 = $140.00

The amount to necessary to pay off the loan early is equal to the sum of the remaining payments less the amount of interest that's included in those payments, or


($500 x 6) - $140 = $2,860
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