Simple Interest

Simple interest is calculated only on the principal amount, or on that portion of the principal amount that remains. It excludes the effect of compounding. Simple interest can be applied over a time period other than a year, for example, every month.

Simple interest is calculated according to the following formula:

${\frac {r\cdot B\cdot m}{n}}$

where

r is the simple annual interest rate

B is the initial balance

m is the number of time periods elapsed and

n is the frequency of applying interest.

For example, imagine that a credit card holder has an outstanding balance of $2500 and that the simple annual interest rate is 12.99% per annum, applied monthly, so the frequency of applying interest is 12 per year. Over one month,

${\frac {0.1299\times \$2500}{12}}=\$27.06$

interest is due (rounded to the nearest cent).

Simple interest applied over 3 months would be

${\frac {0.1299\times \$2500\times 3}{12}}=\$81.19$

If the card holder pays off only interest at the end of each of the 3 months, the total amount of interest paid would be

${\frac {0.1299\times \$2500}{12}}\times 3=\$27.06{\text{ per month}}\times 3{\text{ months}}=\$81.18$

which is the simple interest applied over 3 months, as calculated above. (The one cent difference arises due to rounding to the nearest cent.)

Resources

• Simple and Compound Interest, Book Chapter
• Guided Notes