Effective interest rates are a way of comparing different loans or investments. They put each one’s interest rate into a common form that can then be easily compared with others.

The effective interest rate can be though of in two ways:

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· The amount of interest that would be paid on $1 invested for 1 year.

·
The ratio of the *interest earned on the principal *to the *principal
*over one year.

Dave invests $400 at 5.3% compound interest, with monthly rests. What is the effective interest rate? Monthly rests means the interest is calculated every month. |

Solution |

Let’s use both approaches to calculate the effective interest rate. Approach 1: We want to find out how much interest Dave would earn in a year if he had invested $1. Now since the final amount, A, is the sum of the principal plus the interest built up over the year, the interest is simply: The effective interest rate is just that number expressed as a percentage of the principal: Note how this is higher than the compound interest rate. Approach 2: We want to find the ratio of Once again, the interest is just simply 421.72 – 400 = $21.72. The ratio is simply the interest divided by the principal, which is We need to multiply this by 100 to get a percentage: Use whichever of the two approaches you feel is easier for you. |