Compound Interest

Related to compound amount 

Q. The compound amount of a sum of money in 2 years is Rs. 121000 and in 3 years is Rs. 13310. Find out the sum and the rate of interest per annum. 

Solution : 

Case 1: 

Time (T)= 2 years

C.A.₁ = Rs. 12100

Principle (P)= ?          Rate (R)=?

We know that,

C.A. ₁ = C.A.₁ = P (1+ R/100) ^T1

12100=  P (1+ R/100) ² ......(i)

Case 2:

Time (T) = 3 years

C.A. ₂ = Rs. 13310

Principle (P) = ?        Rate (R) = ?

We know that,

C.A.₂ = P (1+ R/100) ^T2

13310 = P (1+ R/100) ³ .......(ii)

Dividing eqn (ii) by eqn (iP (1+ R/100) ), we get,

13310/12100= [P(1+ R/100)³]/ P(1+ R/100)² 

or,  1.1 = 1 + R/100

or, 1.1= 1+ 0.01R

or, 1.1-1 = 0.01R

or, 0.1/0.01 = R

or, R= 10%

Therefore, the rate of interest is 10%. 

Substituting value of R in eqn(i), we get,

     12100= P(1+10/100) ² 

or, 12100 = P (1.1) ² 

or, P = Rs. 1000

Therefore, the required principle is Rs.1000.