# Simple Interest

The lending and borrowing of money involves the concept of simple interest and compound interest. If you borrow money for certain period of time, you have to return the borrowed sum of money (**Principal**) with some extra money. This extra money is called **Interest**.

The money borrowed is called **principal**. The sum of interest and principal is called the **amount**. The time for which money is borrowed is called **period**.

**Amount = Principal + Interest**

The interest is usually charged according to a specified term, which is expressed as some per cent of the principal and is called the rate of interest for the fixed period of time. This fixed period may be a year, six months, three months or a month and correspondingly the rate of interest is charged annually, semi-annually, quarterly or monthly.

For example, the rate of interest is 5% per annum means the interest payable on Rs. 100 for one year is Rs. 5.

Interest can be of two types:

- Simple Interest
- Compound Interest

### Simple Interest

When the interest is payable on the principal only, it is called simple interest. For example, simple interest on Rs. 100 at 5% per annum will be Rs. 5 each year, that is, at the end of one year, total amount will be Rs. 105. At the end of second year, it will be Rs. 110 and so on.

If P stands for principal, R is the rate percent per annum, T is the number of years, SI is the simple interest and A is the amount, then

**SI = (P × R × T)/100**

Amount can be calculated by adding interest to principal.

Amount = Principal + Simple Interest

A = P + (PRT/100)

**A = P(1 + RT/100)**

### Examples

**Example 1:** Find the simple interest on Rs. 5200 for 2 years at 6% per annum?

SI = (5200 × 6 × 2)/100

= Rs. 624

**Example 2:** At what rate per annum will a sum of Rs. 5000 amount to Rs. 6000 in 4 years?

Here, P = Rs. 5000, A = Rs. 6000, T = 4 years.

So, I = A - P = Rs. 1000

1000 = (5000 × R × 4)/100

R = 5%

**Example 3:** What principal will amount to Rs. 570 at 4% per annum in 3.5 years?

Here, A = 570, R = 4, T = 7/2

A = P + SI = P(1 + RT/100)

570 = P(1 + (4×7)/200)

P = Rs. 500

**Example 4:** A sum of Rs. 1586 is divided among three such parts that amount obtained on these three parts of money after 2, 3 and 4 years, respectively at the rate of 5% per annum remains equal. Find such three parts of the sum?

Let the three parts be Rs. x, Rs. y and Rs. z.

According to question amount obtained is equal,

x + 10x/100 = y + 15y/100 = z + 20z/100

1.1x = 1.15y = 1.2z

x/y = 1.15/1.1 = 23/22

y/x = 1.2/1.15 = 24/25

x : y: z = 276 : 264 : 253

x = 276/793 × 1586 = Rs. 552

y = 264/793 × 1586 = Rs. 528

z = 253/793 × 1586 = Rs. 506

Hence, the three parts are Rs. 552, Rs. 528 and Rs. 506.

**Example 5:** A certain sum of money trebles itself in 5 years simple interest. Find the rate per cent per annum?

Treble means to become three times.

Let Rs. P becomes 3P in 5 years.

Simple interest, SI, is given by

SI = 3P - P = 2P

2P = PRT/100

RT = 200

R = 200/5 = 40

So, rate percent per annum is 40%.

**Example 6: **A certain sum of money invested at some rate of interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?

In 3 years, the amount becomes 3 times the principal.

A = P + I

3P = P + I

I = 2P

The interest is 2 times the principal in 4 years or equal to principal in 2 years.

The interest will be equal to P in 2 years. So interest will be 8P in 16 years.

Amount after 16 years = P + 8P = 9P.

Hence, the required answer is 16 years.

**Example 7:** If simple interest on Rs. 600 increases by Rs. 30, when the rate % increases by 4% per annum, find the time?

SI = PRT/100

When simple interest and rate percent are increased,

SI + 30 = P(R+4)T/100

Subtracting both equations,

30 = PT/100 × (R + 4 - R)

30 = 600T/100 × 4

T = 5/4 = 1.25 years

**Example 8:** If a certain sum of money at simple interest amounts to Rs. 5184 in 2 years and to Rs. 5832 in 3 years, what is the sum and the rate of interest?

Simple interest for one year = 5832 - 5184 = Rs. 648

Let the principle sum be Rs. P.

5184 - P = 2PR/100

5832 - P = 3PR/100

Dividing both the equations,

(5184 - P)/(5832 - P) = 2/3

3(5184 - P) = 2(5832 - P)

15552 - 3P = 11664 - 2P

P = Rs. 3888

For rate,

5184 - 3888 = 2(3888)R/100

R = (1296 × 50)/3888

R = 16.67%

**Example 9:** Out of a certain sum, one-third is invested at 3%, one-sixth at 6% and the rest at 8% If the annual income is Rs. 300, then the original sum is?

Let the sum be Rs. P.

Sum invested at 8% = 1 - (1/3 + 1/6) = 1/2

Sum of interests = Rs. 300

(3P/3 + 6P/6 + 8P/2)/100 = 300

P + P + 4P = 300 × 100

P = Rs. 5000