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Question
A sum of money placed at compound interest compounded annually amounts to Rs 47,610 in 2 years and to Rs 54,751.50 in 3 years. Calculate the rate of interest and the sum.
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Solution
P = x ; r =? ; t= 2 and 3 years ; A= Rs 47,610 (2 years) (3 years)
`"A" = "P" (1 + "r"/100)^"n"`
47610 = x `(1 + "r"/100)^2` ..........(i)
54751.50 = x `(1 + "r"/100)^3` ................(ii)
` therefore ("x" (1 + "r"/100)^3)/("x" (1 + "r"/100)^2) =54751.50/47610 `
⇒`(1 + "r"/100) = 54751.50/47610`
⇒ `"r"/100 = 54751.50/47610 - 1`
⇒ `"r"/100 = (54751.50 - 47610)/47610`
`"r" = 7141.50/47610 xx 100`
r = 15 %
Using (i)
`"x" (1 + "r"/100)^2 =" Rs" 47610`
`"x" (1 + 15/100)^2 = "Rs" 47610`
`"x" (115/100)^2`= Rs 47610
1.3225 x = Rs 47,610
x = Rs 36,000
The sum =Rs 36,000 and rate of interest= 15 %
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