Question

A certain sum of money amounts to Rs. 23,400 in 3 years at 10% per annum simple interest. Find the amount of the same sum in 2 years and at 10% p.a. compound interest.

Answer 1

Let the sum (principle) = X
Given Amount = 23400, R = 10% and T = 3 years

⇒ Interest = `[ "X" xx 10 xx 3 ]/100 = [3X]/10`

Amount = Principle + Interest

23400 = X + `"3X"/10`

X = 18000
Principle = 18000
Now,
Principle = 18000, r = 10% and n = 2 years

`"A" = "P"[ 1 + r/100 ]^n`

`"A" = 18000[ 1 + 10/100 ]^2`

`"A" = 18000[ 11/10 ]^2`

`"A" = 18000[ 121/100 ]`

A = 21780 

The amount of the same sum in 2 years and at 10% p.a. compound interest is 21780.