# Simple interest

The concepts of simple interest and compound interest are of great importance. In this section, we will learn – simple interest basic concepts and simple interest formula.
I have also included questions based on simple interest concepts.
Make sure you have the knowledge of Percentage and profit and loss from before.

### Basic Terms in this concept

Let us understand some terms that we need to know.

1. Principal : The sum of money borrowed or lent is called principal. It is denoted by P.

2. Time: The time period for which money is borrowed or lent.

3. Interest: The amount of  extra money apart from the principal, that we have to pay to the lender is called interest.
There are two types of interests:
i) Simple Interest (SI)
ii) Compound interest (CI)
It is to be noted that the interest can usually be paid annually, half-yearly and quarterly, depending upon the conditions.
In this section we will learn simple interest.

4. Rate percent: It is the rate at which Interest is given.

5. Amount: It is the sum of Principal and interest. Or it the the amount we have to pay to the lender including principal and interest.
Amount = Principal + Interest

For more understanding let us take an example.

Suppose You want to borrow Rs 100 from a person. The person agrees to lend you the money. But If you repay the exact amount to that person after one year, he will have no loss or gain. Then why will he lend the money?

Thus, Interest is added to the borrowed money so that the lender may earn a profit.
Have a look at the conversation in the picture. In this case, Rs 100 is the Principal, Rs 10 is the interest, Rs 110 the Amount, and the time duration is 1 year.

### Simple Interest Definition

It is usually calculated on the original principal for any duration of time.
Or in other words, the Principal is the same for every year. It is denoted by SI.
Simple interest formula,
SIMPLE INTEREST (SI) = \frac { P\times R\times T }{ 100 }
Here,
P = Principal
R = rate percent per annum
T = time for which money is lent/borrowed

### Formulas

1.  Simple interest formula :
Simple Interest (SI) = \frac { P\times R\times T }{ 100 }

2.  For finding Principal:
Principal (P) = \frac { 100\times SI }{ R\times T }

3. Calculating Rate percent:
Rate% = \frac { 100\times SI }{ P\times T }

4. Calculating Time:
Time = \frac { 100\times SI }{ P\times R }

5. To find SI for distinct rate of interest for different periods.
Suppose,
⇒The rate for
1st { t }_{ 1 } years = { R }_{ 1 } %
⇒and rate for
2nd { t }_{ 2 } years = { R }_{ 2 } %
⇒also the rate
for 3rd { t }_{ 3 } years = { R }_{ 3 } %

#### The total SI for ({ t }_{ 1 }+{ t }_{ 2 }+{ t }_{ 3 }) years = \frac { P(R_{ 1 }{ t }_{ 1 }+{ R }_{ 2 }{ t }_{ 2 }+{ R }_{ 3 }{ t }_{ 3 }) }{ 100 }

6. When the interest is paid “Half-yearly
The rate of interest gets half.
i.e R ⇒ \frac { R }{ 2 }
And time will be twice.
t ⇒2t
7. When interest is paid “Quarterly”
then,
Rate gets one-fourth

R⇒ \frac { R }{ 4 }
And  time will be four times
t⇒ 4t

8. When a sum of money becomes “x” times in “t” years, then the rate of interest is given by
Rate= \frac { 100(x-1) }{ t } %

9. The difference between SI for a certain { P }_{ 1 } for time { T }_{ 1 } and rate { R }_{ 1 } and another sum { P }_{ 2 } for time { T }_{ 2 } and rate { R }_{ 2 } is given by:
difference of the SI =\frac { { P }_{ 2 }{ R }_{ 2 }{ T }_{ 2 }-{ P }_{ 1 }{ R }_{ 1 }{ T }_{ 1 } }{ 100 }
1.

### Questions based on Simple interest formulas

Question 1: The amount of Rs 2500 is borrowed at 5% rate per annum for 2 years. Find the simple interest and the amount.
Solution: Given, P = Rs 2500
R= 5%
t= 2 years
SI = ?
We know,
SIMPLE INTEREST (SI) FORMULA = \frac { P\times R\times T }{ 100 }

= \frac { 2500\times 5\times 2 }{ 100 }

= Rs 250
therefore, simple interest is Rs 250
and Amount = Principal + Interest
=2500+250
= Rs 2750

## If the time is given in month and days

Question 2: If Rs 7200 is borrowed at 10 % rate and for 9 months. Find the simple interest.
Solution: Given, P = Rs 7200
R= 10%
and t= 9 months = \frac { 9 }{ 12 } = \frac { 3 }{ 4 } year
SI = ?
We know,
SIMPLE INTEREST (SI) = \frac { P\times R\times T }{ 100 }

= \frac { 7200\times 10\times \frac { 3 }{ 4 } }{ 100 }

= Rs 540
therefore, simple interest is Rs 540

Question 3:  Rs 10950 is borrowed at 2 % rate and for 200 days. Find the simple interest.
Solution: Given, P = Rs 10950
R= 2%
t= 200 days = \frac { 200 }{ 365 } year
SI = ?
We know,
SIMPLE INTEREST (SI) = \frac { P\times R\times T }{ 100 }

= \frac { 10950\times 2\times \frac { 200 }{ 365 } }{ 100 }

= Rs 120
therefore, simple interest is Rs 120

If “a sum of money becomes x times” type of questions

Question 4 : A sum of money becomes \frac { 7 }{ 6 } times of itself in 3 years at a certain rate of SI. Find the rate% per annum.
Solution :
1st method
When a sum of money becomes “x” times in “t” years, then the rate of interest is given by
Rate= \frac { 100(x-1) }{ t } %  {here x =  \frac { 7 }{ 6 }}

= \frac { 100(\frac { 7 }{ 6 } -1) }{ 3 } %

=5\frac { 5 }{ 9 } %
2nd method
Here Principal = P
Amount =  \frac { 7 }{ 6 } P (because it is given Principal becomes \frac { 7 }{ 6 }  of itself)
and time = 3 years
thus,
SI = Amount – Principal
= \frac { 7 }{ 6 } P – P
=  \frac { 1 }{ 6 } P
Now
Rate% = \frac { 100\times SI }{ P\times T }

= \frac { 100\times \frac { 1 }{ 6 } P }{ P\times 3 }

=5\frac { 5 }{ 9 } %
Therefore Rate % is 5\frac { 5 }{ 9 } %

Question 5 : A sum of money doubles itself in 10 years at a certain rate of SI. Find the rate% per annum.
Solution :
1st method
When a sum of money becomces “x” times in “t” years, then the rate of interest is given by
Rate= \frac { 100(x-1) }{ t } % {here x =2}

= \frac { 100(2 -1) }{ 10 } %

=10 %
2nd method
Here Principal = P
Amount =  2P (because it is given Principal doubles itself)
and           time = 10 years
thus,
SI = Amount – Principal
=  2P – P
=  P
Now
Rate% = \frac { 100\times SI }{ P\times T }

= \frac { 100\times P }{ P\times 10 }

=10 %
Therefore Rate % is 10%

Question based on finding total SI.

Question 8: Sumit borrowed Rs 8000 from a person.He borrowed the money at the rate of 6% per annum for the first 3 years, 9% p.a for the next 5 years and 13% p.a beyond eight years. Find the total interest paid by him.
Solution: Given,
P = Rs 8000
{ R }{ 1 } = 6%    { t }{ 1 } = 3 year
{ R }{ 2 } = 9%    { t }{ 2 } = 5 year
{ R }{ 3 } = 13%  { t }{ 3 } = 3 year [ as 13% rate beyond eight years. And total year is 11 year. 6% for 3 year and 9% for 5 years. The year left is 11-(3+5) = 3 years]
Total  SI=

#### \frac { P(R_{ 1 }{ t }_{ 1 }+{ R }_{ 2 }{ t }_{ 2 }+{ R }_{ 3 }{ t }_{ 3 }) }{ 100 }

=\frac { 8000[6\times 3+9\times 5+13\times 3] }{ 100 }
=80×102
=Rs8160
therefore total SI is Rs 8160

To find the principal

Question 9 : What will be the sum of money given if the simple interest is Rs 500 at 5% rate p.a for 2 years?
Solution: Given,
SI = Rs 500
t=2 year
R = 5%
then
Principal (P) = \frac { 100\times SI }{ R\times T }

= \frac { 100\times 500 }{ 5\times 2 }

=Rs 5000

To find the rate%

Question 10: What will be the rate % if Principal is Rs7300 ,SI= Rs 365 and time is 1 year?
Solution: Given P= Rs 7300
SI= Rs365
t =1 year
Rate% = \frac { 100\times SI }{ P\times T }

= \frac { 100\times 365 }{ 7300\times 1 }

R=5%