# How Effective Financing Rates Work

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The effective financing rate is the actual annual rate at which your financial obligations will grow. It is this rate, and not what may be printed on your contract, that will determine how much you will actually owe on your credit card bill, car loan or any other kind of debt. It is therefore absolutely crucial to understand how an effective financing rate works.

## Simple Interest

When you lend or borrow money, you use a simple interest rate to determine how much you owe or are owed by the borrower, if the duration of the loan is less than the compounding period of the interest rate. The idea is actually very simple. Say you borrow \$1,000 from a bank and the annual interest rate is 10 percent with annual compounding. If you pay the loan back in six months, you will owe exactly half of 10 percent, or 5 percent, of \$1,000 in interest. You will therefore pay back the original \$1,000 plus \$50 in interest. With simple interest, the interest expense equals: (number of months divided by 12) X interest rate X principal.

## Compound Interest

Now assume you pay the same loan after two full years. This time you must use the compound interest formula because the loan term exceeds the compounding period. The total debt now equals principal multiplied by 1 plus the interest rate, raised to second power. This equals \$1,000 * (1+0.1)^2 = \$1,210. What happened here is pretty simple. At the end of the first year, you owe principal plus 10 percent, which equals \$1,100. During the second year, this sum grows by another 10 percent. Ten percent of \$1,100 equals \$110, which you must now add to \$1,100 and your total debt is now \$1,210. If you fail to use the compound interest formula and assume that your debt will grow by \$100 every year, you will arrive at the mistaken result of \$1,200.

## Monthly Compounding

Things get just a touch more complicated with your credit card bill or car loan. There, you are usually quoted an annual rate, but the compounding period will be monthly. If your statement includes an effective annual rate, take that into account. If the statement does not specify such a rate, calculate it. Assume that your annual rate is 12 percent with monthly compounding. The formula for effective annual rate is (1 + interest rate per compounding period) ^ number of compounding periods per year - 1

The monthly rate equals 12 percent divided by 12, which is one percent; this is your interest rate per compounding period. The effective annual rate therefore equals (1 + 1%) ^ 12 - 1 . In other words 1,01 raised to the 12th power, or multiplied by itself 12 times or 12.68%

## General Guidelines

As a general rule, the more frequently a loan compounds, the greater the interest that will accumulate. A loan with an annual rate of 10 percent with daily compounding has a greater effective rate than another loan with a 10 percent annual rate that compounds monthly. When borrowing money, you want the lowest possible effective annual rate. When investing money, however, you want the highest effective annual rate, since the faster your money grows, the better off you are.