One of the most important concepts of commercial mathematics is interest. Now interest can be of two types – simple interest and compound interest. Here we will be primarily focused on the concept of simple interest. We will learn the meaning and concept of simple interest, simple interest formula and other terminology related to it. Let us get started!

## Simple Interest

The entire concept of simple interest is based on the time value of money. This means that money has a current value in the present, known as present value and another value in the future known as future value. So essentially, it costs to borrow or loan some money. And vice-versa if you invest money in a time deposit, you earn money. This amount is known as interest.

Take for example the case of Mr. A. He wished to start a business and so he approached a bank for a loan. The bank was happy to comply. The agreed to loan him an amount of Rs 10,000/- for 2 years. Now at the end of two years, he will have to return the money to the bank. But he cannot just pay back the 10,000/-. Remember it costs to borrow money. So he must pay interest at the agreed 8% per annum.

### Simple Interest Formula

Before we learn the simple interest formula, let us see the terms related with the formula. First is the rate of interest (R). This is the rate at which interest will be charged per annum. From the example above, we can identify that the rate is 8%. The next is the term or the duration of the arrangement. We call this the time period or the term (n or t). It is generally expressed in years since the rate is per annum. In the above example, the term is 2 years.

Then we have the principal amount (P). This is the initial amount of the loan, or the initial amount invested. In the above example, the principal amount is the amount of loan given by Mr. A, which is 10,000/-. Then we have the Future Value, or the amount (FV or A). This is the amount that Mr. A gets at the end of the term, i.e after 2 years. This Amount includes the Principal and the Simple Interest. Now let us take a look at some important formulas with respect to Simple Interest.

- Simple Interest = (PÂ Ã— RÂ Ã— T)Â Ã· 100
- Amount = SI + P
- A = {(PÂ Ã— RÂ Ã— T)Â Ã· 100} + P

Where

SI | Simple Interest |

A | Amount/Future Value |

P | Principal Amount |

R | Rate of Interest per annum |

T | Time in years |

## Solved Examples

Q: Mr. B invested 50,000/- in a bond that pays 5% interest. What will be his accumulated interest at the end of 3 years?

Ans: Here we simply have to calculate the interest amount. So we will directly apply the formula,

Simple Interest = (PÂ Ã— RÂ Ã— T)Â Ã· 100Â = (50000 Ã— 5 Ã— 3)Â Ã· 100

Simple Interest = 7500/-

Q: Mr A had invested 1000/- for 4 years. At the end of the period, he got back Rs 1250/-. Find the rate of interest

SI = A -P = 1250-1000 = 250

250 =Â (PÂ Ã— RÂ Ã— T)Â Ã· 100 = (1000Â Ã— RÂ Ã— 4)Â Ã· 100

R = 6.25%

I get a different answer for first example.

I got Q1 as 20.5

median 23 and

Q3 26