# Simple vs. Compound Interest Calculation

Interest is the charge against the use of money by the borrower. The same is profit earned by the lender of money. The amount which is invested in a bank in order to earn interest is called principal. The interest rate is normally expressed in percentage and represents the dollar interest earned per $100 of principal in a specific time, usually a year. Simple interest and compound interest are the two types of interest based on the way they are calculated.

## Simple Interest

Simple interest is charged only on the principal amount. The following formula can be used to calculate simple interest:

Simple Interest (I_{s}) = P × i × t |

Where,

**P** is the principle amount;

**i** is the interest rate per period;

**t** is the time for which the money is borrowed or lent.

### Example 1

Suppose $1,000 were invested on January 1, 2010 at 10% simple interest rate for 5 years. Calculate the total simple interest on the amount.

__Solution__

We have, Principle

P= $1,000 Interest Ratei= 10% per year Timet= 5 years Simple Interest I_{s}= $1,000 × 0.1 × 5 = $500

## Compound Interest

Compound interest is charged on the principal plus any interest accrued till the point of time at which interest is being calculated. In other words, compound interest system works as follows:

- Interest for the first period charged on principle amount.
- For the second period, its charged on the sum of principle amount and interest charged during the first period.
- For the third period, it is charged on the sum of principle amount and interest charged during first and second period, and so on ...

It can be proved mathematically, that the interest calculated as per above procedure is given by the following formula:

Compound Interest (I_{c}) = P × (1 + i) ^{n} – P |

Where,

**P** is the principle amount;

**i** is the compound interest rate per period;

**n** are the number of periods.

### Example 2

Consider the same information as given in Example 1. Now calculate the total compound interest on the amount invested.

__Solution__

We have, Principle

P= $1,000 Interest Ratei= 10% per year No. of Periodsn= 5 Compound Interest I_{c}= $1,000 × ( 1 + 0.1 )^5 − $1,000 = $1,000 × 1.1^5 − $1,000 = $1,000 × 1.61051 − $1,000 = $1,610.51 − $1,000 = $610.51

Written by Irfanullah Jan