# Simple Interest

In this chapter, you will be introduced to the concept of borrowing money and the simple interest that is derived from borrowing.

You will also be introduced to terms such as principal, amount, rate of interest, and time period. Through these terms, you can calculate simple interest using the simple interest formula.

Once you get the concepts right, you will no longer require a simple interest calculator.

Check-out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.

## Lesson Plan

 1 What is Simple Interest? 2 Thinking Out of the Box! 3 Tips and Tricks 4 Solved Examples on Simple Interest 5 Interactive Questions on Simple Interest

## What is Simple Interest?

Simple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies on the original principal amount, with the same rate of interest for every time cycle.

When we invest our money in any bank, the bank provides us an Interest on our amount. The interest applied by the banks is of many types one of them is Simple Interest.

### What is a Loan?

A loan is an amount that a person borrows from a bank or a financial authority to fulfill their needs. Loan examples include home loans, car loans, education loans, and personal loans.

A loan amount is required to be returned by the person to the authorities on time with an extra amount, which is usually the interest you pay on the loan.

## What is the formula to calculate simple interest?

Simple interest is calculated with the following formula

 $$S.I = P \times R \times T$$

Where $$P$$ = Principal

$$R$$ = rate of interest in % per annum

$$T$$ = Time, usually calculated as the number of years

### Principal:

The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by $$P$$.

### Rate:

Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be $$5%$$, $$10%$$ or $$13%$$, etc. The rate of interest is denoted by $$R$$.

### Time:

Time is the duration for which the principal amount is given to someone. Time is denoted by $$T$$.

Example:

Let's go back to Michael's father. We said that he had borrowed $1000 from the bank. What we didn't tell you then was that the rate of interest was 5%. What would the simple interest be if the amount is borrowed for 1 year? Similarly, calculate the simple interest if the amount is borrowed for 2 years, 3 years, and 10 years? Solution: Principal Amount =$1000

Rate of Interest = 5% = $$\dfrac{5}{100}$$

Simple Interest
1 Year $\text { S.I }= \\1000 \times \frac{5}{100} \times 1\\= 50$
2 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 2\\=100$
3 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 3\\=150$
10 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 10\\=500$

When a person takes a loan from a bank so he/she has to return the principal borrowed plus the interest amount so that the total amount returned is called Amount.

 $$\text{Amount = Principal + Simple Interest}$$
 $$A = P + S.I.$$
 $$A = P + PRT$$
 $$A = P( 1 + RT)$$

Now, prepare a table for the above question adding the amount to be returned after the given time period.

 Simple Interest Amount 1 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 1\\=50$ $\text { A }= \\1000 + 50 \\=1050$ 2 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 2\\=100$ $\text { A }= \\1000 + 100 \\ =1100$ 3 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 3\\=150$ $\text { A }= \\1000 + 150 \\= 1150$ 10 Year $\text { S.I }=\\1000 \times \frac{5}{100} \times 10\\=500$ $\text { A }= \\1000 + 500 \\= 1500$

Think Tank
1. What if a bank provides you an interest such that your money doubles every day, if you invested 1 $on day 1, in how many days you will become a billionaire? 2. Will you invest if a bank provides a negative rate of interest? Example: Mary invested a sum of$2000 in a fund at a rate of 8% per year. For how much time does she invest the money so that she will $3000 in return. Solution: Amount to be returned to Mary =$3000

The principal amount invested = 2000 Rate of interest = 8% Let the time for which she invested the money be $$T$$ \begin{align} A &= P(1 + RT)\\[0.2cm] 3000 &= 2000 \times (1 + \dfrac{8}{100} \times T)\\[0.2cm] \dfrac{3000}{2000} &= 1 + \dfrac{8}{100} \times T\\[0.2cm] \dfrac{3}{2} - 1 &= \dfrac{8}{100} \times T\\[0.2cm] \dfrac{1}{2} &= \dfrac{8}{100} \times T\\[0.2cm] \dfrac{1}{2} \times \dfrac{100}{8} &= T\\[0.2cm] T &= \dfrac{1}{2} \times \dfrac{100}{8}\\[0.2cm] T &= 6.25 \text{years}\\[0.2cm] \end{align}  Mary has to invest the money for 6.25 years ### Simple Interest Calculator ## What Types of Loans use Simple Interest? Most banks these days apply compound interest on loans because in this way banks get more money as interest from their customers, but this method is more complex and hard to explain to the customers. On the other hand, calculations become easy when banks apply simple interest methods. Simple interest is much useful when a customer wants a loan for a short period of time, for example, 1 month, 2 months, or 6 months. When someone goes for a short term loan using simple interest, the interest applies on a daily or weekly basis instead of a yearly basis. Consider that you borrowed10000 on simple interest at a 10% interest rate per year, so this 10% a year rate divide into a rate per day which is equal to $$\dfrac{10}{365} = 0.027%$$

So you have to pay $2.73 a day extra on$10000

Tips and Tricks
1. To find the time period, the day on which money is borrowed is not taken into account, but the day on which money has to be returned is counted.
2. The rate of interest is the interest on every $100 for a fixed time period. 3. Interest is always more in the case of compound interest as compared to simple interest. 4. The formula or methods to calculate compound interest is derived from simple interest calculation methods. 5. Rate of interest is always kept in fractions in the formula. ## Solved Examples  Example 1 Robert purchased a car worth$48000, he borrowed the money from the bank at 10% per annum for a period of 4 years. How much amount he has to pay after the period.

Solution

The principal value for the car is 48000 The rate of interest is 10% The time period given is 4 years Using the formula for amount \begin{align} A &= P(1 + RT)\\[0.2cm] A &= 48000 \times (1 + \dfrac{10}{100} \times 4)\\[0.2cm] A &= 48000 \times (1 + \dfrac{2}{5})\\[0.2cm] A &= 48000 \times (\dfrac{7}{5})\\[0.2cm] A &= 67200 \end{align}  Robert has to pay67200
 Example 2

If Maria borrowed a sum of $46500 for a period of 21 months at 20% per annum, how much simple interest will she pay? Solution The principal amount is$46500

The rate of interest is 20% = $$\dfrac{20}{100}$$

The time period given is 21 months = $$\dfrac{21}{12}$$ years

Using the formula for interest

\begin{align} I &= P \times R \times T\\[0.2cm] I &= 46500 \times \dfrac{20}{100} \times \dfrac{21}{12}\\[0.2cm] I &= 16800 \end{align}

 Maria going to pay $16800  Example 3 David borrowed a certain sum that amounts to$4000 in four years, and $4500 in five years. What were the principal amount and the rate of interest? Solution Let the principal value be $$P$$ and the rate of interest be $$R$$ Amount in 4 years =$4000

Amount in 5 years = 4500 \begin{align} A &= P(1 + RT)\\[0.2cm] 4000 &= P \times (1 + R\times 4)\\[0.2cm] 4500 &= P \times (1 + R\times 5)\\[0.2cm] \dfrac{4000}{4500} &= \dfrac{(1 + R\times 4)}{(1 + R\times 5)}\\[0.2cm] \dfrac{8}{9} &= \dfrac{(1 + R\times 4)}{(1 + R\times 5)}\\[0.2cm] R &= \dfrac{1}{4} = 25 \%\\[0.2cm] \\[0.2cm] 4000 &= P \times (1 + \dfrac{1}{4} \times 4)\\[0.2cm] 4000 &= P \times (1 + 1)\\[0.2cm] 4000 &= 2 \times P\\[0.2cm] P &= 2000 \end{align} 2000 was borrowed at 25% rate of interest

## Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

## Let's Summarize

We hope you enjoyed learning about simple Interest with the simulations and practice questions. Now you will be able to easily solve problems on simple interest rate formula, simple interest calculator, simple interest examples, simple interest meaning.

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## 1. What is the use of simple interest?

Simple interest is used in cases where the amount that is to be returned requires a short period of time. So, car loans, mortgages, and education loans use a simple interest calculator.

## 2. What are the types of simple interest?

Simple interest is of two types ordinary simple interest and exact simple interest. In the ordinary simple interest, a year is considered of 360 days while calculating the interest while in exact simple interest a year is considered of 365 (or 366 days of a leap year) days. Both methods use the same formula to calculate simple interest.

## 3. Are home loans simple or compound interest?

Home loans take a long time to repay, so the interest added by the lender is usually a compound interest.

## 4. Are car loans simple or compound interest?

Car loans or auto loans use simple interest to calculate the interest. The borrower agrees to pay the money back, plus a flat percentage of the amount borrowed.

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