Question

# On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.

CAT 2021

A
B
C
D
##### Rs 1,600
Solution

Correct option is

(C)

Let Principal = P

rate of interest = r%

acc. to ques ,

$P(1+r)^{3}-P&space;=&space;1456------eqn&space;(1)$ [end of 3 years]

$P(1+r)^{2}-P&space;=&space;880------eqn&space;(2)$ [end of 2 years]

dividing both eqns

$3r^{2}+3r+r^{3}/r^{2}+2r=1456/880$

after solving , we get $55r^{2}+74r-17=0$

r= 1/5 , hence r = 1/5*100 = 20%

after putting value of r in any eqn , we get ,

P=2000

Hence , C is the correct option