# How Effective Financing Rates Work

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When entering into a financing agreement, it is important to bear in mind the difference between the nominal and effective financing rates. When working with compounding interest, the effective interest rate can be significantly higher than the nominal financing rate, which, in turn, means financing can be much more costly than anticipated.

## Compounding Interest

Compounding interest refers to interest that builds upon itself. In other words, during each compounding period, interest is paid on both the original principal and the interest accrued during the previous compounding periods. For example, if a man borrows \$100 at a 6 percent financing rate, the amount owed will be \$106 after the first compounding period and \$112.36 after the second period. The additional \$0.36 from the second compounding period comes from the fact that the interest from the first compounding period accrues interest.

## Nominal Interest Rate

The nominal interest rate in a financing agreement is the interest rate stated in the agreement. For example, if an agreement says that 6 percent interest will be charged monthly for a period of three years, the nominal financing rate is 6 percent; however, the actual effective financing rate will be somewhat higher due to the compounding interest.

## Compounding Period

The compounding period refers to the amount of time that passes between each instance of interest being applied to the debt being financed. For example, if interest is accrued monthly, the compounding period is one month. This means that each month, interest is accrued on both the original amount borrowed and any interest accrued during previous compounding periods.

## Effective Financing Rate Calculation

To calculate the effective financing rate from a nominal interest rate, use the equation r = (1 + i/n)^n - 1, where r is the effective interest rate, i is the nominal interest rate and n is the number of compounding periods. For example, if the nominal interest rate is 6 percent and there are six compounding periods, the effective interest rate is equal to: r = (1 + .06/6)^6 - 1 = 6.15 percent.

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