Question

A certain sum of money invested at compound interest compounded annually amounted to Rs 5,082 after 2 years and to Rs 5,590.20 after 3 years. Calculate the rate of interest and the sum invested.

Answer 1

Here, r =? P = x (say) 

T = 2 years and 3 years 

A= Rs 5,082 in 2 years and Rs 5,590.20 in 3 years. 

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

`5082 = "x" (1 + "r"/100)^2 ` ..................   (i)

`5590.20 = "x" (1 + "r"/100)^3` ................(ii)

Dividing (ii) by (i)

`("x"  (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) = 5590.20/5082` 

`=> 1 + "r"/100 = 5590.20/5082`

`=> "r"/100 = 5590.20/5082 - 1`

`=> "r"/100 = (5590.20 - 5082)/5082`

`=> "r"/100 = 508.20/5082`

`=> "r" = 508.20/5082 xx 100`

⇒ r = 10%

using (i)

`"x" (1 + "r"/100)^2 = "Rs"  5082`

`"x" (1 + 10/100)^2 = "Rs"  5082`

`"x" xx 11/10 xx 11/10 = "Rs"  5082`

`"x" xx 121/100  = "Rs"  5082`

`"x" = "Rs"  (5082 xx 100)/121`

x = Rs 4200

Hence, rate of interest= 10°10 and sum invested =Rs 4,200.