REAL LIFE INTERE$T.

How do banks really compute interest? In preparing these pages the author called most of the banks in his town and asked how interest was computed. Most of them carefully explained that they did what was most advantageous to the customer whereas many of their competitors did something else. Curiously, all of them did exactly the same thing. Interest, according to the banks, is
To illustrate what this means, suppose the bank pays 4% interest and you deposit $250 on March 7. Your $250 starts accumulating interest at the rate of 4/365 percent each day, and this is compounded each day. However, the interest is not credited to your account until April 1. Thus if you withdraw your funds on March 30, you will receive the same $250 you deposited. But if you withdraw your money on April 1 you will receive (1 + .04/365)24 $250 or $250.65 (assuming the bank rounds down) because your money has been earning interest for 24 days.

This means that your money is earning interest which is being compounded daily, but the interest is not credited to your account until close of business on the last day of the month.

How do banks advertise interest rates? The standard way of advertising interest rates is as APY. This stands for Annual Percentage Yield. If the base (or simple) rate is 4%, then the APY is the interest you earn when this rate is compounded daily. To compute this, think of starting with a balance of B dollars and depositing it for a year. At the end of the year, your balance has grown to (1 + .04/365)365 B dollars. If you subtract your principle B from this number, you will be left with the amount of interest you earn. Thus the interest rate is

(1 + .04/365)365 - 1

which you must convert to a percent by multiplying by 100. This works out to be 100 (1.04081 - 1) = 4.08%.

Here is a machine for computing the APY from a base rate. Type an interest rate into the box labeled "base rate" and press the "compute" button. The APY will appear in the appropriate box. [Note: User input is disabled for the second box!]

Base Rate: %
COMPUTE APY
 %

Exercise

You open a bank account with $100 on April 5. The bank pays a rate of 5% which is compounded daily and posted monthly. You close your account on July 13. Which of the following formulas expresses the ending balance?

(1 + .05)98 $100. (1 + .05/365)98 $100.
(1 + .05)86 $100. (1 + .05/365)86 $100.

<- Check Answer
<- See Explanation

© 1997,1998 Robby Robson, Oregon State University.