# CLASS-8SIMPLE INTEREST

SIMPLE INTEREST–

Simple interest is a very basics thing which is to be described for finding interest of a given principal within a stipulated time. Let us go over some terms and formula that you learnt in the previous class. Interest (I) is to be considered as the additional amount paid by the borrower to the lender for the use of a sum of money. Principal (P) is considered as the sum of money lent, borrowed or invested. Time (T) - the duration for which the sum of money is lent or invested, usually in years. Rate (R) is to be considered as the interest paid on \$ 100 per unit of time, usually per annum (p.a).  Amount (A) is to be considered as the sum of the principal and the interest.

There are some formula are given below –

Amount (A) = Principal (P) + Interest (I)

Principal (P) = Amount (A) – Interest (I)

Interest (I) = Amount (A) – Principal (P)

Simple Interest (I) – The interest paid on the original sum of money borrowed or invested.

Principal (P)  X  Rate (R)  X  Time (T)

Interest (I) = -------------------------------------

100

Rate (R) X Time (T)

Amount (A) = Principal (P) ( 1 +  ---------------------- )

100

Example.-

1) Find the simple interest on \$ 12,000 for 5 years at the rate of 1) 7.5% per annum, and 2) 1.5% per month. Find the amount in each case.

Answer) As per the given condition, if he put \$ 100 then in 1 year he should get interest around \$ 7.5

then in, if he put \$ 1 then in 1 year he should get the interest around =

\$ 7.5

------------                                                                                                                                                          100

then in, if he put \$ 12000 then in 1 year he should get the interest around

7.5 X 12000

= -----------------                                                                                                                                                       100

in, if he put \$ 12000 then in 5 year he should get the interest around

7.5 X 12000 X 5

=  --------------------- =   \$ 4500……………….(1)                                                                                                                          100

if he put \$ 100 then in 1 month he should get interest around \$ 1.5

then in, if he put \$ 1 then in 1 month he should get the interest around

\$ 1.5

=  -------------                                                                                                                                                         100

then in, if he put \$ 1 then in 12 month ( 1 year) he should get the interest around

\$ 1.5 X 12

=  ---------------                                                                                                                                                        100

then in, if he put \$ 12000 then in 1 year he should get the interest around

1.5 X 12 X 12000

= ----------------------

100

in, if he put \$ 12000 then in 5 year he should get the interest around

1.5 X 12 X 12000 X 5

= -------------------------- =  \$ 10800……………….(2)

100

Another way –

As per the given condition, he is getting the interest around \$ 7.5 per annum, so now we have to calculate the obtained interest over \$ 12000 for 5 years.

Here, Principal (P) = \$ 12000, Rate (R) = 7.5 %, Time (T) = 5 years

Principal (P) X Rate (R) X Time (T)

As per the formula, Interest (I) = --------------------------------

100

12000 X 7.5 X 5           450000

= ------------------- = ------------ =  \$ 4500 ……………(1)

100                    100

As per the given condition, he is getting the interest around \$ 1.5 per month, so now we have to calculate the obtained interest over \$ 12000 for 5 years.

So, first we have to calculate the interest per annum, so we get =  1.5 X 12 = 18 % per annum

Here, Principal (P) = \$ 12000, Rate (R) =  18 %, Time (T) = 5 years

Principal (P) X Rate (R) X Time (T)

As per the formula, Interest (I) = --------------------------------

100

12000 X 18 X 5          1080000

= ------------------ = ------------ = \$ 10800 ……………(2)   (Ans.)

100                    100

2) Find the simple interest on, \$ 1500 from 25 April 2018 to 5

2

December 2019 at the rate of 5 ------- % per annum.

3

Ans.) The number of days from 25 April 2018 to  5 December 2019 are given below –

25th Apr'18 – 30th Apr'18 = 6 days

1st May’18 – 31st May’18 =  31 days

1st Jun’18 – 30th Jun’18 =  30 days

1st Jul’18 – 31st Jul’18 = 31 days

1st Aug’18 –  31st Aug’18 = 31 days

1st Sep’18 – 30th Sep’18 = 30 days

1st Oct’18 – 31st Oct’18 = 31 days

1st Nov’18 – 30th Nov’18 = 30 days

1st Dec’18 – 31st Dec’18 = 31 days

1st Jan’19 – 31st Jan’19 = 31 days

1st Feb’19 – 28th Feb’19 = 28 days

1st Mar’19 – 31st Mar’19 = 31 days

1st Apr’19 – 30th Apr'19 = 30 days

1st May’19 – 31st May’19 =  31 days

1st Jun’19 – 30th Jun’19 =  30 days

1st Jul’19 – 31st Jul’19 = 31 days

1st Aug’19 –  31st Aug’19 = 31 days

1st Sep’19 – 30th Sep’19 = 30 days

1st Oct’19 – 31st Oct’19 = 31 days

1st Nov’19 – 30th Nov’19 = 30 days

1st Dec’19 – 5th Dec’19 = 5 days

Total days = 6 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 5 = 590 days

590          118

If we calculate total obtained days in year = -------- = -------- years

365           73

Now we have to find out the desired interest where, Principal (P) = \$ 1500, Time (T) = 118/73 years,

2

Rate (R) =  5 ------- %  =  17/3 %

3

Principal (P) X Rate (R) X Time (T)

As per the formula, Interest (I) = -------------------------------

100

17          118

1500 X ------- X --------

3           73

= -------------------------------------

100

1500 X 17 X 118

= -------------------- =  \$ 137.4        (Ans.)

3 X 73 X 100

3) Find the simple interest on, \$ 2500 from 20th Oct'19 to 10 Apr'20

1

at the rate of  3 ------- % per month.

2

Ans.) The number of days from 20 October 2019 to 10 April 2020 are given below –

20th Oct’19 – 31st Oct’19 = 12 days

1st Nov’19 – 30th Nov’19 = 30 days

1st Dec’19 – 31st Dec’19 = 31 days

1st Jan’20 – 31st Jan’20 = 31 days

1st Feb’20 – 29th Feb’20 = 29 days  ( Feb'2020 is considered as Lip year )

1st Mar’19 – 31st Mar’19 = 31 days

1st Apr’19 – 10th Apr = 10 days

Total days = 12 + 30 + 31 + 31 + 29 + 31 + 10 = 174 days

174

If we calculate total obtained days in year = --------- years

365

1

Given Rate  =  3 ------- % = 7/2 % per month, if we convert this given

2

per month rate into per annum

7

Rate, then it will be = --------- X 12 months  =  42 %

2

Now we have to find out the desired interest where, Principal (P) = \$ 2500, Time (T) = 174/365 years,

Rate (R) = 42 % per annum

Principal (P) X Rate (R) X Time (T)

As per the formula, Interest (I) = ------------------------------

100                                                                                                                                       174

2500 X 42 X ---------

365

= ----------------------------------

100

2500 X 42 X 174

=  -------------------- =   \$ 500.55      (Ans.)

365 X 100