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Question
A certain sum of money invested at compound interest compounded annually amounted to Rs 26,450 in 2 years and to Rs 30,417.50 in 3 years. Calculate the rate of interest and the sum invested.
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Solution
Here, r =? P = x (say)
T = 2 years and 3 years
A= Rs 26,450 in 2 vears and Rs 30,417.50 in 3 years.
`"A" = "P" (1 + "r"/100)^"n"`
`26450 = "x" (1 + "r"/100)^2` ........(i)
`30417.50 = "x" (1 + "r"/100)^3` ........ (ii)
Dividing (ii) by (i)
`("x" (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) = 30417.50/26450`
`=> 1+ "r"/100 = 30417.50/26450`
`=>"r"/100 = 30417.50/26450 -1`
`=>"r"/100 = (30417.50 - 26450)/26450`
`=>"r"/100 = 3967.50/26450`
`=> "r" = 3967.50/26450 xx 100`
⇒ r = 15 %
using (i)
`"x" (1 + "r"/100)^2 = Rs 26450`
`"x" (1 + 15/100)^2` = Rs 26450
`"x" xx 23/20 xx 23/20` = Rs 26450
`"x" xx 529/400` = Rs 26450
`"x" = "Rs" (26450 xx 400)/529`
x = Rs 20,000
Hence, rate of interest= 15 % and sum invested =Rs 20,000
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