A sum of money placed at compound interest compounded annually amounts to Rs 31,360 in 2 years and to Rs 35,123.20 in 3 years. Calculate the rate of interest and the sum.

#### Solution

P = x ; r = ? ; t= 2 and 3 years ; A = Rs 31,360 ( 2 years) and Rs 35, 123.20 ( 3 years)

`"A" = "P" (1 + "r"/100)^"n"`

`31360 = x (1 + "r"/100)^2` .........(i)

`35123.20 = "x" (1 + "r"/100)^3` ..............(ii)

`therefore ("x" (1 + "r"/100)^3)/(x (1 + "r"/100)^2) = 35123.20/31360`

⇒ `(1 + "r"/100) = 35123.20/31360`

⇒ `"r"/100 = 35123.20/31360 - 1`

⇒ `"r"/100 = (35123.20 - 31360)/31360`

`"r" = 3763.20/31360 xx 100`

r = 12%

Using (i)

`"x" (1 + "r"/100)^2` = Rs 31,360

`"x" (1 + 12/100)^2` = Rs 31,360

`"x" (112/100)^2` = Rs 31,360

1 .2544 X = Rs 31,360

x = Rs 25,000

The sum = Rs 25,000 and rate of interest = 12 %.