Question

sum of money becomes ₹18000 in 2 years and ₹40500 in 4 years on compound

interest. Find the sum.​

Answer 1

Answer:

The sum is Rs.8,000 and rate of interest is 50 per cent per year

Step-by-step explanation:

Formula for compound interest is

A = P*(1+R/100)^T

A = final amount

P = initial sum/principal

R = rate of interest per cent per year

T = number of years

[This is assuming annual compounding]

We are given A = 18000 when T = 2

Thus,

18000 = P*(1+R/100)^2                     ....(Eqn 1)

Also,

40500 = P*(1+R/100)^4          .......(Eqn 2)

Dividing Eqn 2 by Eqn 1, we get:

40500/18000 = (1+R/100)^2

2.25 = (1+R/100)^2

(1+R/100) = $\sqrt{2.25}$

1+R/100 = 1.5              

R/100 = 0.5        

R=50

Using R in Eqn (1), we get

18000 = P*(1+50/100)^2

18000 = P*(1.5)^2

18000 = 2.25*P

P = 18000/2.25

P = 8000

(You can also substitute for R in Eqn 2 and obtain the same result)