Effective Interest Rates

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.

Effective interest rate question

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 the interest gained over a year on his principal to the principal:

                                                

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.