# Simple Interest

Go back to  'Commercial Math'

Ever borrowed money from a friend or relative and they said that you would have to return the amount after a year with $$10\%$$ interest? Well, that means that you will have to return the amount borrowed along with an additional sum of $$10\%$$ of the borrowed amount after a year. This additional sum is called the interest amount, and here we will explore the concept of simple interest.

## What are the terms related to simple interest?

\begin{align} \text{Principal }(P) &= \text{The original sum of money that is borrowed is called } PRINCIPAL \\\\ \text{Interest }(I) &= \text{The additional sum of money which the borrower has to pay back to the lender as a fee is called }INTEREST\\\\ \text{Amount }(A) &= \text{The total sum of money that the borrower has to pay back to the lender is called }AMOUNT \end{align}

Thus,

\begin{align} \text{Amount} = \text{Principal} + \text{Interest} \end{align}

The annual rate of interest is the interest charged per year expressed as a percentage of the principal. ‘$$\text{per year}$$’ is also called as ‘$$\text{per annum}$$’.
Usually, the rate of interest is expressed as a percentage per year. However, it can also be expressed as a percentage per month/week/day etc

## Simple interest formula

This interest is called ‘$$\text{SIMPLE INTEREST}$$’. We can directly use the \begin{align} {(P \times R \times T)} \over 100\end{align} formula to find the simple interest. Here, $$P$$ denotes the principal, $$R$$ denotes the rate of interest and $$T$$ denotes the time.

Using an example to clarify. If you borrowed $$₹5000$$ from a bank with an interest rate of $$7 \%$$ for a period of $$8$$ years, then the Simple Interest would be calculated as:

\begin{align} \text{Interest } &= {{(P \times R \times T)} \over 100} \\\text{Interest } &= {{(5000 \times 7 \times 8)} \over 100} \\ &= {280000 \over 100} \\ &= ₹2800 \end{align}

## Tips and Tricks

• The rule of $$72$$ tells you how long it will take for your money to double. Using the rule of $$72,$$ we can find the number of years to double your money by simply dividing $$72$$ by the rate of interest. For example, at $$12 \%$$ compounded interest rate your money will double in $$72 \div 12 = 6 \text{ years}.$$
• The time duration over which an interest rate is applicable is referred to in many different terms. Sometimes it is called “per annum” or “annual” or “per year”. All of these mean you’ll get the given rate of interest over a period of one year. Semi-annual is $$6$$ months. While quarterly is $$3$$ months duration.
• Sometimes the question will state an annual rate of interest (say $$12 \%$$). But it will also say that the interest is compounded at an interval which is different from a year (say semi-annually). Here, you must adjust the interest rate as well as time periods accordingly.
• In this case, since the time interval is half a year, also take interest as half the annual rate. So, calculate time period in $$6\text{-month}$$ chunks and interest rate as $$12 \div 2 = 6 \%.$$
The rate of interest and each time period must be of the same duration.

1. In how many years will a sum of $$₹800$$ at $$10 \%$$ per annum become $$₹1280?$$
2. At what rate of simple interest will $$₹1000$$ grow to $$₹1200$$ in two years?