The Ins and Outs of Figuring Loan Interest

Pretty much everyone knows that interest is the extra amount you have to pay to a lender in addition to paying back the amount you borrow. But most people (even some experienced business managers) are not entirely clear regarding how interest is figured. When you borrow money, you agree to a method of interest accounting, whether you understand the method or not.

Suppose someone offers to loan you $100,000 for one year, and he tells you that he will charge you 6 percent interest. How much will you have to pay him one year from today? He does mean 6 percent per year, right? Certainly he doesn't mean 6 percent per month. Whatever agreement he's offering, get it in writing.

When you take out a loan, the lender should ask you to sign a legal instrument called a note. This document states the principal of the loan ($100,000), the maturity date (one year from the present date), the interest rate per period (6 percent per year), and other provisions concerning my rights as a lender in the event that you default — that is, if you don't comply fully with the conditions of the loan. The lender may ask for collateral, or security for the loan, which generally is an asset you own that the lender could take possession of and sell to pay off your debt in the event you default. Or he may ask for a lien to be filed on property you own as security for the loan (which is done in mortgage loans). The lender may require a co-signer — a second person who signs the note and is liable for the debt if you default.

How much do you owe on this loan one year later? The lender wants his money back ($100,000) plus 6 percent of the principal, which is $6,000 interest. So you owe him $106,000 at the maturity date of the loan. You had the use of $100,000 for one year and pay $6,000 in interest for that privilege. The lender gave up the use of the money for one year and earned $6,000 interest income.

Say that you need the money for two years instead of one. Because of the longer time period, the lender might demand a higher interest rate, say 6.5 percent. At the end of the first year you pay him $6,500 interest, and at the end of the second year you pay him $106,500, which consists of $6,500 interest for the second year and the $100,000 payoff of the principal.

Changing the example ever so slightly can have profound implications. Suppose that you need to borrow $100,000 for two years and you agree to pay 6.5 percent annual interest. However, you don't want to make any interest payment until the maturity date, which is two years later. How much do you owe then? The 6.5 percent interest rate is based on the premise that the lender receive interest at the end of each year. If that doesn't happen the first year, the nonpayment of interest becomes a loan within a loan; you have to pay 6.5 percent interest on this "second loan" in addition to the original $100,000 loan principal. The principal balance at the start of the second year, therefore, is $106,500. The lender's entitled to 6.5 percent interest on the $106,500 principal balance during the second year. Obviously, the interest for the second year will be more than the interest owed for the first year.

This adding on, or bumping up, of the principal balance of a loan because of the nonpayment of interest at the end of the period is called compounding, or compound interest. The balance owed is compounded by the amount of the unpaid interest, and this higher balance is the basis for computing interest during the next period. (This term also applies when you are on the receiving end of interest, such as when you invest money in a savings account.) In the example of the two-year loan, the interest for the second year, based on the compounded balance brought forward from the end of the first year, is:

$106,500 Principal Balance x 6.5% Interest Rate = $6,922.50 Second Year Interest

What if you borrowed the money for five years, with no interest payments along the way? How much would you owe at the end of five years (assuming the lender's willing to make the loan for five years with no interest payments until maturity)? You would owe $137,000 (rounded off a little) at the end of the fifth year, for a total of $37,000 interest. How do you know whether this is correct? You could trust the lender; after all, he's in the business of loaning money and he ought to know what he's doing. But it may be better to calculate whether the amount of interest seems in the ballpark. Without compounding, the interest would be $6,500 per year (based on the original $100,000 borrowed), and for five years this would be $32,500 total interest. The extra $4,500 interest that the lender says that you owe at the end of five years because of compounding seems reasonable. Of course, you could ask your accountant to double-check the number, or you could use a handheld calculator to do so.