Interest – Simple Interest and Compound Interest

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 amount 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

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.

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 (P1) = Rs.22,500

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

Rate (R1) = 14%

Simple Interest(I1) =   (P x T x R/100)    =  22500 x 14/ 100  x 21/4 = Rs. 16,537.50

‘B’ has given to ‘C’

Principal (P2) = Rs.22,500

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

Rate (R1) = 15%

Simple Interest(I2) = (P x T x R/100)= 22500 x 15 /100  x 21/4 = Rs. 17,718.75

Difference = I2 – I1 = 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 P1 = 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 (I1) = (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

P2 = 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 (I2) = (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

P3 = 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 (I3) = (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 (P4) = Rs. (67,000-12,000)/- = Rs. 50,000/-,

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

Interest (I4) =  (P x T x R/100)  =  50000 x 9.75 /100 x 151/365=  Rs. 2,016.78

Total interest = I1 + I2 + I3 + I4 = 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.