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प्रश्न
A sum of money placed at compound interest compounded annually amounts to Rs 31,360 in 2 years and to Rs 35,123.20 in 3 years. Calculate the rate of interest and the sum.
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उत्तर
P = x ; r = ? ; t= 2 and 3 years ; A = Rs 31,360 ( 2 years) and Rs 35, 123.20 ( 3 years)
`"A" = "P" (1 + "r"/100)^"n"`
`31360 = x (1 + "r"/100)^2` .........(i)
`35123.20 = "x" (1 + "r"/100)^3` ..............(ii)
`therefore ("x" (1 + "r"/100)^3)/(x (1 + "r"/100)^2) = 35123.20/31360`
⇒ `(1 + "r"/100) = 35123.20/31360`
⇒ `"r"/100 = 35123.20/31360 - 1`
⇒ `"r"/100 = (35123.20 - 31360)/31360`
`"r" = 3763.20/31360 xx 100`
r = 12%
Using (i)
`"x" (1 + "r"/100)^2` = Rs 31,360
`"x" (1 + 12/100)^2` = Rs 31,360
`"x" (112/100)^2` = Rs 31,360
1 .2544 X = Rs 31,360
x = Rs 25,000
The sum = Rs 25,000 and rate of interest = 12 %.
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