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Interest is an extra amount of money along with the initial amount of money to be returned by a borrower, to a lender providing an initial amount of money has taken before by him.

**In an elaborated way:**

Suppose a person’ X’ has given certain amount of money on request of ‘Y’ for his expenses or to start a business or for any other reason, ‘X’ demands ‘Y’ to pay an extra amount other than the amount borrowed, when he returns to ‘X’. The demanded amount is the **INTEREST**.

If ‘B’ borrows an amount of Rs. 100/- from ‘A’. Now it is clear that ‘B’ has to return the same amount i.e.Rs.100/- to ‘A’. But ‘A’ demanded some extra amount in addition to Rs.100/- e.g; ‘A’ need Rs.10/- extra (a total of Rs.110/-), if ‘B’ want to pay after a certain period of time, then the extra amount against ‘B’’s requirement which is called **INTEREST.**

Interest has some regulations. The amount of interest depends on the rate to which the amount is borrowed as well as time period.

**In detail:**

For example two persons ‘X’ and ‘Y’ are the lender and borrower respectively. ‘Y’ borrowed an amount of Rs.100/- from ‘X’ at the rate of 10% per annum and agrees to pay the amount exactly for 1 year.

Here we have to notice three things (or components), they are:

**Lending or borrowing amoun**t is called PRINCIPAL (P)→ currency in rupees/dollar etc.**Rate or percentage**is called RATE OF INTEREST (R) → is % per annum**“Number of years borrowing for”**is called TIME (T) → in years

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**Interest can be calculated using the formula:**

I = (P x T x R/100)

I – where ‘I’ is called SIMPLE INTEREST denoted by letter I or S.I.

Amount is the sum of principal and the interest; that is written as,

A = P + I, where ‘A’ is amount, ‘P’ is principle and ‘I’ is simple interest.

**SIMPLE INTEREST:**

This is obtained by the formula: I = (P x T x R/100)

Where Amount (A) = Principle (P) + Interest (or simple interest) (I)

**Example 1:**

Sandeep has borrowed Rs. 10,000/- from Maneesh at a rate of 12% per annum. Calculate the interest and amount to be paid by Sandeep to Maneesh after 2 years?

**Solution:**

Principal (P) = Rs. 10,000/-

Rate of interest (R) = 12%

Time period (T) = 2 years

Interest (I) = (P x T x R/100) = 10000 x 2 x 12/100 = Rs.2,400/-

Amount (A) = P + I = Rs. (10,000 + 2,400) = Rs. 12,400/-.

Therefore Sandeep has to pay an interest Rs. 2,400/-, and a total of Rs. 12,400/- to Maneesh at the end of 2 years.

**Example 2:**

Amar borrowed a loan of Rs. 18,000/- from a financier at the rate of 15% per annum. How much is the interest and what amount has he to pay the financier after 3 years 4 months from the date of commencement of loan?

**Solution:**

Principal ( P ) = Rs.18,000/-

Rate of interest (R) = 15%

Time period (T) = 3 years and 4 months

Now we have to covert the time into years, that is 3 4/12 years = 3 1/3 or 10/3 years

Another way of converting years and months into pure years is as follows;

3 years and 4 months = 36 months + 4 months = 40 months = 40/12 = 10/3 years

Interest (I) = (P x T x R/100) = 18000 x 15/100 x 10/3 = Rs. 9,000/-

Amount (A) = P + I =Rs. 18,000 + Rs. 9,000 = Rs. 27,000/-

Therefore Amar has to pay the financier an interest of Rs.9000/- and an amount of Rs.27,000/- at the end of 3 years 4 months from the date of commencement of loan.

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**Example 3:**

‘A’ borrowed certain amount from ‘B’ for simple interest. ‘A’ agreed to pay double amount to ‘B’ exactly after 5 years. What is the rate of interest?

Or

A person borrowed certain amount for simple interest, for what rate of interest the amount is doubled after 5 years?

**Solution:**

Let the Principal = P

Time =5 years

Rate = ?

Amount = 2P (given)

We know that A= P + I implies I = A – P =2P – P = P

Interest (I) = (P x T x R/100)

R = I x 100 / P x T = P x 100/ P x 5 = 20%

Therefore the rate of interest = 20%

**Example 4:**

In how many years Rs. 56,000/- becomes Rs. 75,152/- at the rate of 7.2% simple interest?

**Solution:**

Principal= Rs. 56,000/-

Amount = Rs. 75,152/-

Interest = A – I =Rs.( 75,152 – 56,000 ) = Rs. 19,152/-

Rate of interest = 7.2%

From I = (P x T x R/100) , we get

T = I x 100 / P x R = 19152 x 100 /56000 x 7.2 = 19/4 = 4 years = 4 years and 9 months.

Therefore the required time is 4 years 9 months.

**Example 5:**

Find Principal when it amounts to Rs. 27,000/- at 12.5% simple interest for 4 years?

**Solution:**

Let Principal = Rs. **x** /-

Amount = Rs. 27,000/-

Interest = A – I = Rs.(27,000 – x )

Rate = 12.5%

Time = 4 years

I = (P x T x R/100) = x x 4 x 12.5/100

x x 4 x 12.5/100 = 27000 – **x**

x x 4 x 12.5 = 100 x ( 27000 – **x** )

50 x = 2700000 – 100 **x**

50 **x** + 100 **x** = 2700000

150** x** = 2700000

x = 2700000/150

x = Rs. 18000/-

Therefore the Principal is Rs. 18,000/-

**Example 6:**

A person borrows a sum of Rs. 22,800/- as loan from a bank on 05/03/2013 at a rate of 14.4%. After certain time he earns money and wants to return back the loan amount. If he pays the amount on 23/10/2015, what amount he has to pay the bank to clear the loan?

**Solution:**

Principal (P) = Rs.22,800/-

Rate of interest (R) = 14.4%

Time period (T) = from 05/03/2013 to 23/10/2015,

We have to count the number of days month wise as follows

From 05/03/2013 to 31/03/2013 : 26 days

From 01/04/2013 to 30/04/2013 : 30 days

From 01/05/2013 to 31/05/2013 : 31 days

From 01/06/2013 to 30/06/2013 : 30 days

From 01/07/2013 to 31/07/2013 : 31 days

From 01/08/2013 to 31/08/2013 : 31 days

From 01/09/2013 to 31/09/2013 : 30 days

From 01/10/2013 to 31/10/2013 : 31 days

From 01/11/2013 to 31/11/2013 : 30 days

From 01/12/2013 to 31/12/2013 : 31 days

From 01/01/2013 to 31/12/2014 : 365 days

From 01/01/2015 to 31/10/2015 : 273 days

From 01/10/2013 to 23/10/2014 : 23 days

Here we have to convert the total number of days into years, adding all number of days, we get

Time = 962 days = 962/365 years (since 1 year = 365 days)

Interest (I) = (P x T x R/100) = 22800 x 14.4 / 100 x 962/365 = Rs. 8,653.26

Amount (A) = P + I = Rs. (22,800 + 8,653.26) = Rs. 31,453.26

Hence the person has to pay the bank an amount of Rs. 31,453.26 for to close the loan account on 23/10/2015..

**Example 7:**

‘A’ has given Rs. 12,500/- to ‘B’ at a rate of 14% per annum, on the same day ‘B’ has given the same amount to ‘C’ at 15% per annum. After 5 years 3 months ‘C’ returns the amount to ’B’ and ‘B’ also returns to ‘A’. Calculate the amount left with ‘B’ after his settlement.

**Solution:**

‘A’ has given to ‘B’

Principal (P_{1}) = Rs.22,500

Time = 5 years and 3 months = 63/12 = 21/4 years

Rate (R_{1}) = 14%

Simple Interest(I_{1}) = (P x T x R/100) = 22500 x 14/ 100 x 21/4 = Rs. 16,537.50

‘B’ has given to ‘C’

Principal (P_{2}) = Rs.22,500

Time = 5 years and 3 months = 63/12 = 21/4 years

Rate (R_{1}) = 15%

Simple Interest(I_{2}) = (P x T x R/100)= 22500 x 15 /100 x 21/4 = Rs. 17,718.75

Difference = I_{2} – I_{1} = Rs. 17,718.75 – Rs. 16,537.50 = Rs. 1,181.25

Therefore ‘B’ got a benefit by Rs. 1,181.25.

**Example 8:**

A person brought Rs. 1,10,000/- from a financier on 02/02/2015 for simple interest, on 15/04/2016 it amounts to Rs. Rs.1,25,000/-. What is the rate of interest?

**Solution:**

Principal = Rs.1,10,000/-

Amount = Rs.1,25,000/-

Interest = Rs.15,000/-

Time = from 02/02/2015 to 15/04/2016 =26 + 366 + 15 = 407 days = years

Rate of interest = ?

R = I x 100/ P x T = 15000 x 100 / 110000 x 407/365 = 15000 x 100 x 365/ 110000 x 407 = 12.23%

**Example 9:**

Ram and sham deposited of Rs. 60,000/- and Rs. 40,000/- respectively in two different banks. Ram got Rs.82,500/- after 3 years and Sham got Rs. 60,800/- after 4 years. Who got benefited? Find the rate of interest given in each case.

**Solution:**

Ram’s Principal = Rs.60,000/-

Amount (A) = Rs.82,500/

Time = 3 years

Rate = ?

We know that, A = P + I

I = A – P = Rs.(82,500 – 60,000)/- = Rs.22,500/-

Using the formula, I = (P x T x R/100) we can get ‘R’ value

Hence R = I x 100 / P x T = 22500 x 100 / 60000 x 3 = 12.5%

Therefore Ram got an interest for 12.5%

Sham’s Principal =Rs. 40,000/-

Amount = Rs. 60,800/-

Time = 4 years

Rate = ?

AS above, A = P + I

I = A – P = Rs.(60,800 – 40,000)/- = Rs.20,800/-

Using the formula, I = (P x T x R/100) we can get ‘R’ value

Hence R = I x 100 / P x T = 20800 x 100 / 40000 x 4 = 13%

Therefore Sham got an interest of 13%

From these two values we conclude that Sham got benefited since he got 0.5% more.

**Example 10 ****:**

Mrs. Malathi availed a personal loan of Rs. 85,000/- in a bank for simple interest on 01/04/2013, and the rate of interest is 9.75% for 1 year. She paid Rs. 10,000/- on 01/07/2013,Rs.8,000/- on 1/09/2013 and Rs. 12,000/- on 01/11/2013 to the bank. What amount she has to pay on 31/03/2014?

**Solution :**

Principal P_{1} = Rs.85,000/-

Rate of interest = 9.75%

Here we have to split the time period since she paid the amount in three installments

Now the time period = 01/04/2013 to 30/06/2013 = 91 days = 91/365 years

Interest (I_{1}) = (P x T x R/100) = 85000 x 9.75 /100 x 91/365 = Rs. 2066.20

On 01/07/2013 she paid Rs. 10,000/-, then the Principal becomes

P_{2 }= Rs. (85,000-10,000)/- =Rs. 75,000/-

Rate = 9.75%

Time period = from 01/07/2013 to 31/08/2013 = 62 days = 62/365 years

Interest (I_{2}) = (P x T x R/100) = 75000 x 9.75 /100 x 62/365 = Rs.1242.12

Again she paid Rs. 8,000/- on 01/09/2013, hence the principal becomes

P_{3} = Rs. (75,000-8,000)/- = Rs.67,000/-, Rate = 9.75%

Time period = From 01/09/2013 to 31/10/2013 = 61 days = 61/365 years

Interest (I_{3}) = (P x T x R/100) = 67000 x 9.75 /100 x 61/365 = Rs. 1,091.73

She paid an amount of Rs. 12,000/- on 01/11/2013.

Principal (P_{4}) = Rs. (67,000-12,000)/- = Rs. 50,000/-,

Time period = from 01/11/2013 to 31/03/2014 = 151 days Rate = 9.75%

Interest (I_{4}) = (P x T x R/100) = 50000 x 9.75 /100 x 151/365= Rs. 2,016.78

Total interest = I_{1} + I_{2} + I_{3 }+ I_{4} = Rs. (2066.20+1242.12+1091.73=2016.78) = Rs. 12,833.66

Total amount paid by Mrs. Malathi = Rs. (10,000+8,000+12,000)/- = Rs. 30,000/-

Amount to be paid = Rs. (85,000-30,000+12,833.66) = Rs. 67,833.66

Therefore she has to pay an amount of Rs. 67,833.66 on 31/03/2014 to clear her loan.

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