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Question
A sum of money placed at compound interest compounded annually amounts to Rs 26,460 in 2 years and to Rs 29,172.15 in 4 years. Calculate the rate of interest and the sum.
Solution
P = x; r = ? ; t= 2 and 4 years ; A= Rs 26,460 (2 years) and Rs 29, 172.15 (4 years)
`"A" = "P" (1 + "r"/100)^"n"`
`26460 = "x" (1 + "r"/100)^2` .............(i)
`29172.15 = "x" (1 + "r"/100)^4` ..........(ii)
`therefore ("x" (1 + "r"/100)^4)/("x" (1 + "r"/100)^2) = 29172.15/26460`
⇒ `(1 + "r"/100)^2 = 194481/176400`
⇒ `(1 + "r"/100)^2 = (441/420)^2`
⇒ `1 + "r"/100 = 441/420`
⇒ `"r"/100 = 441/420 - 1`
⇒ `"r"/100 = (441 - 420)/420`
r = `21/420 xx 100`
r = 5%
Using (i)
`"x" (1 + "r"/100)^2` =Rs 26460
`"x" (1 + 5/100)^2` =Rs 26460
`"x" (105/100)^2` = Rs 26460
1.1025 x = Rs 26,460
x = Rs 24,000
The sum = Rs 24,000 and rate of interest = 5 %
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