Simple interest is made easy with the following.

Maturity Value `A` = Principal `P + ` Interest `P R T `

`=P (1+R+R+R...T` times)

Note: R is the (interest rate in percentage)/100.

The interest is calculated on the principal for each of the time period in `T`. That is, the interest `PR` is added `T` times.

Once the above is understood, the equation is easily derived.

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A person takes a loan:

The principal is `1,00,000` coins

interest rate is `10%` per annum

loan duration (time) is `1` year

interest in one year = principal `xx` time `xx` interest rate `//100`

= `1,00,000 xx 1 xx 10 //100`

` = 10,000`coins

At the end of loan duration, the person returns maturity value

maturity value = principal `+` interest

`100000+10000 = 1,10,000`coins

A person takes a loan:

The principal is `1,00,000` coins.*Simple interest* rate is `10%` per annum

loan duration (time) is `3` years.

interest in one year = principal `xx` interest rate `xx` time `//100`

= `1,00,000 xx 10 xx 3 //100`

` = 30,000`coins

At the end of loan duration, the person returns maturity value

maturity value = principal `+` interest

`100000+30000 = 1,30,000`

Note: This form of interest is called *simple interest*.

Which of the following is a meaning for the word "simple"?

- plain and basic form; presented without any complexity
- plain and basic form; presented without any complexity
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The answer is "plain and basic form; presented without any complexity".

What is the term used to refer to "interest that is charged without any complexity"?

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is "simple interest".

**Simple Interest** : Interest charged for a loan duration only on the principal is simple interest.

Let us understand how interest rate is specified.

Interest rate is given as `10%` per annum. What does that mean?

- `10%` means for every `100` coins, the interest is `10` coins
- "per annum" means interest is for every year
- both the above
- both the above

The answer is "both the above"

Students may find it difficult to memorize all the formulas for simple interest. This is listed for reference, but in the next page, these are explained. *No need to memorize any of them.*

principal `P`

Interest Rate `R`

Number of time periods `T`

Maturity value or amount `A`

Simple interest `S= PRT//100`

Maturity value `A = P + PRT//100`

Rate of interest `R = (A-P)xx100//(PT)`

Time period `T = (A-P)xx100//(PR)`

Principal `P = Axx 100 // (1+RT)`

One need not memorize any formulas. Quickly follow through the *story* to recall formulas on the fly.

• Interest is calculated as percentage of the principal. So, `I = PR // 100` for every time period

• Interest is calculated for a number of time periods. So, `I = PRT //100` for all the time periods

• The borrower has to return principal and the interest, which is the maturity value.*Maturity Value `A` = Principal `P + ` Interest `P R T // 100`*

There are `4` variables (A, P, R, T) in this equation. In a problem, `3` of these `4` variables are given and this formula is a form of *linear equation of one variable (algebra)* to solve for the unknown variable.

The principal `3000` coins is returned as `4080` coins in `3` years. Find the simple interest rate per annum.

- `10%`
- `12%`
- `12%`

The answer is "`12%`".

Given that

Principal `= 3000` coins

Maturity Value `= 4080` coins

Loan duration `= 3 years`*substituting the given values in the equation*

`A = P+PRT//100`

`4080 = 3000+ 3000 xx R xx 3 //100`

`1080 = 90R`

`R = 12%`

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