Simple interest and solved examples with shortcut method

Simple interest 

Principal:

When you first deposit money in a saving account or when you borrow some money from another person, bank, or any financial institution that amount is known as the principal.

Interest:

The extra amount paid by the borrower to the lender for the use of the amount lent is called interest.

Simple Interest:

When we borrow some amount from another person for a certain period of time we have to pay him some extra money is called interest. This interest is the same for the same period of time. This is called simple interest or SI.

Formulae:

I. S.I =  PRT ÷ 100

Where p is principal, R is the rate of interest, T is time.

When SI is added to Principal it is changed into amount A.

ii. P + SI = A

iii.SI = A- P

Case i: If SI, R, and T are known

P = (SI × 100) ÷ (R × T)

Case ii:  If S.I, T, and P are known

R = (SI × 100) ÷ (P × T)

Case iii:  When SI, P, and R are known

T = (SI × 100) ÷ (R × P)

Ex.1 If SI for 6 years be equal to 30% of the Principal then in how many years it will be equal to the 2 times of principal.

Sol. Let principal = 100  Simple interest ∝ T

30% in 6 years

thus,

30 = 6

1 = 6/30

200 = 200 * (6/30) = 40 years

Ex.2By which rate any principal becomes 5 times within 20 years.

Sol. The let amount is 300 and the principal is 100

S.I = A-P =  200

200 = (10*R*20)/100

R = 10% Ans.

Ex.3A principal was lent at SI at a certain rate for 2 years. Had it lends at 3% it would have path 300 Rs. more than finding the Principal.

Sol. Rate = 20%    after 2 years = 40%

       Rate =23%     after 2 years = 46%

       rate = 46-40 = 6

6% = 300

100 = (300*100)/6 = 5000 Ans.

Case iv. If some of the money becomes n1 times in time T1 then how many years T2 it becomes n2 times. Then we use

 (n1 – 1)/t1 = (n2-1)/ t2

 Installment:

A sum of money due as one of several equal payments for something spread over an agreed period of time.

Equal installment: (100 A) / 100 T + RT [(t-1)/2]

Questions based on Simple interest with short tricks:

Ex.1 Find S.I on Rs. 5000 at the rate of interest of 5% per year for 5 years.

Sol. Method 1

S.I  = (PRT)/100 = (5000*5*5)/100 = 1250 Rs.

Method 2.

100 Rs. at 5% in 1 year  = 5 Rs.

100 Rs. at 5% in 5 year = 25

In simple interest same amount is credited per year

1%  of 5000 Rs. is 50. 

5% interest for 5 years means 25%

Thus simple interest is 25*50 = 1250 Ans.

Ex.2 On a certain sum of money at 6% per year Simple interest is Rs. 324 for years. Find a sum of money.

Sol. Method 1.

 P = (SI * 100)/RT

= (324/100)/6*3

Rs. 1800 Ans

Method 2.

P       T         R

100 1 year   6

100 3 years 18

*18            *18

1800 Rs.     324 Ans

Ex.3 At what rate of interest per annum, S.I on Rs. 1000 will be Rs. 343 in 7 years?

Sol. Method 1. 

SI = PRT/100

343 = (1000*R*7)/100

R = 4.9%

Method 2

1000  7 year   343

1000  1 year  49

100 =  4.9% Ans

Ex.4 A certain sum of money becomes 5/2 times of itself in 5 years. Find the rate of interest?

Sol. (n-1) = rt/100

(5/2 - 1) = (R*5)/100

3/2 = t/20

R = 30% Ans

Ex.5 A sum of money is lent at simple interest. After 5 years it's S. I become 2/5 of the principal. Find the rate of interest?

Sol. n = rt/100

2/5 = (r*5)/100 

r = 8% Ans

Ex.6 The difference of simple interest on a certain sum of money for 4 years and 6 years is Rs. 1125 if the rate of interest is 5% p.a.find sum of money.

Sol. Method 1 

P = [(SI1 - SI2) * 100]/R(T1-T2)

P = (1125 * 100)/(5*2)

P = Rs. 11250

Method 2

T= 2 year R=5%

SI = RT%

10% = Rs. 1125

100% = (1125/10) * 100

Rs. 11250 Ans

Ex.7 Ram lent Rs. 9000 in two Parts to Danish and Deepak one at 5% p.a. and another at 8% p.a. respectively. After 2 years he gained a combined interest rate of 7% p.a. Find the money lent at 8% p.a.

Sol. Method 1 

Let sum at 8% p.a is x

(x*8*2)/100 + [(9000-x)5*2] /100 = (9000*7*2)/100

6x = 36000

x = Rs. 6000

Method 2

P1/P2 = (8-7)/(7-5)

P2 = (2/3)*9000 = 6000 Rs. Ans

Ex.8 A sum of money becomes 4 times in 30 years at a certain rate of simple interest. In how many years it will become 6 times of itself at the same rate of interest.

Sol. (n1 - 1)/t1 = (n2-1)/t2

(4-1)/30 = (6-1)/t2

t2= 50 years Ans

Ex.9 Ram lent some money to Mohan at 6% p.a. for 5 years and the same money to Gaurav at the same rate of interest for 3 years. If Ram gains Rs. 1920 as total interest from Mohan and Gaurav. Find the money lent to each.

Sol. P = [(SI1+SI2)*100]/(T1+T2)R

P = (1920 * 100)/6*8 = Rs. 4000

Method 2

T= 8 year R = 6%

SI = RT%

48% = 1920

1% = 40

100%= 4000 Ans

Ex.10 What equal installment of annual payment will discharge a debt that is due as Rs. 848 at the end of 4 years at 4% per annum simple interest.

Sol. Use formula  of installment

(100*848)/ 100*4 + 4*4[(4-1)/2]

= (100*848)/ 424

= Rs. 200  Ans

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