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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.
Solution
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.
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