Understanding the Mathematics of Personal Finance

Prepayment Penalties

When you take a loan, the lender has legitimate up-front costs in preparing the paperwork, setting up the account, monitoring the payments, and so on. In the case of a mortgage, as shown in Chapter 4, the lender usually manages to charge you for these costs. In the case of an auto loan, there might not be any up-front costs. Instead, the lender estimates his or her costs and wraps them into the interest rate for the loan. This is equivalent to what I have shown at the end of Chapter 4; it’s just not shown explicitly—you’re quoted an interest rate and that’s that.

Suppose you were to acquire some money you didn’t think you’d have, or you have the savings, or for whatever reason you decide to pay the loan off early. The lender not only loses expected interest, but he or she also loses the part of the up­front costs that haven’t been recaptured yet. In this case, it’s not unreasonable for the lender to charge you these unrecaptured costs in the form of a prepayment penalty.

How a prepayment penalty is calculated must be spelled out in the original loan agreement. Unfortunately, historically, some lenders have looked on this situation as an opportunity to grab some extra profits. In many states, laws have been enacted to limit the prepayment penalty that lenders can demand.

One way of keeping you from realizing just how much the prepayment penalty is costing you is to keep you from realizing just how much your outstanding balance is. Table 5.1 shows a simple 3-year car loan. The principal is \$15,000 and the interest rate is 8.0%. The monthly payment is \$470.05. As you can see by looking at the balance column, the balance correctly goes to 0 after 36 payments.

If you add up all the interest payments, you get \$1,921.64. Now add this to the principal and you get \$16,921.64. This is of course the same number you get if you add up all the payments (or equivalently, multiply one payment amount by the number of payments). This number is shown at the top of the right-hand column, which I’ve labeled fake balance. If you deduct the 36 payments from this amount, one per month, you again get to a 0 balance at the end of 36 months.

If you are presented with the fake balance column as a payment schedule instead of the real balance column, you are not being cheated in that you are paying the correct monthly payment and paying off the loan at the correct time. But, along the way, you have no idea what your real outstanding balance is.

Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy, by

Lawrence N. Dworsky

Table 5.1 Auto Loan with “Interest Up-Front” Balance

 Pmt Nr Balance (\$) Interest (\$) Fake balance (\$) 0 15,000.00 0.00 16,921.64 1 14,629.95 100.00 16,451.59 2 14,257.44 97.53 15,981.55 3 13,882.45 95.05 15,511.50 4 13,504.95 92.55 15,041.46 5 13,124.94 90.03 14,571.41 6 12,742.39 87.50 14,101.36 7 12,357.30 84.95 13,631.32 8 11,969.63 82.38 13,161.27 9 11,579.38 79.80 12,691.23 10 11,186.53 77.20 12,221.18 11 10,791.07 74.58 11,751.14 12 10,392.96 71.94 11,281.09 13 9,992.20 69.29 10,811.05 14 9,588.77 66.61 10,341.00 15 9,182.65 63.93 9,870.96 16 8,773.82 61.22 9,400.91 17 8,362.27 58.49 8,930.86 18 7,947.97 55.75 8,460.82 19 7,530.91 52.99 7,990.77 20 7,111.07 50.21 7,520.73 21 6,688.44 47.41 7,050.68 22 6,262.98 44.59 6,580.64 23 5,834.69 41.75 6,110.59 24 5,403.54 38.90 5,640.55 25 4,969.52 36.02 5,170.50 26 4,532.60 33.13 4,700.45 27 4,092.77 30.22 4,230.41 28 3,650.01 27.29 3,760.36 29 3,204.30 24.33 3,290.32 30 2,755.62 21.36 2,820.27 31 2,303.94 18.37 2,350.23 32 1,849.26 15.36 1,880.18 33 1,391.54 12.33 1,410.14 34 930.77 9.28 940.09 35 466.93 6.21 470.05 36 0.00 3.11 0.00

For example, just after your twelfth payment, 1 year after you took the loan, your outstanding balance is \$10,392.96. With no prepayment penalties, this is what it should cost you to pay off the loan. Typically, you’d make the twelfth payment and the outstanding balance payment at the same time. Also, lenders are usually prorating interest by the day, so depending on which day you actually want to pay off the loan, your exact payment should be close to but not exactly this number.

Now, look at the fake balance for the same day—\$11,281.09. This is almost \$1,000 more than the actual balance, about 8.5% more. If the lender quotes a number such as \$10,700 to pay off the loan after your twelfth payment and your only infor­mation is the fake balance payment schedule, you can’t see that you’re being charged about \$300 prepayment penalty. You ’ ll see some information such as “unearned interest” on the payoff document as an explanation of why your payoff number is lower than the fake balance.

This latter type of calculation is sometimes called a precomputed loan calculation.

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