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a sum of money let out at compound interest at a certain rate per annum becomes three times of itself in 5 years. Find in how many years will the money become 27 times of itself at same rate of interest per annum?

Answer :

Let amount(A) = 3x Let sum(P) = x =>A = P (1 + R/100)^t =>3x = x (1 + R/100)^5 =>3 = (1 + R/100)^5 A = 27x P = x =>27x = x (1 + R/100)^t =>27 = (1 + R/100)^t =>(3)^3 = (1 + R/100)^t =>(1 + R/100)^(3*5) = (1 + R/100)^t t = 15 years
kvnmurty
sum accumulated with compound interest = P (1 + r/100)⁵ = 5 P
   =>  1 + r/100 = 5¹/⁵ = 1.3797
   r/100 = 0.3797
   r = 37.97%

   in 27 years:  P (1 + 37.97/100)^n = 27 * P
         =>  n Log 1.3797  =  log 27
                   n = Log 27 / Log 1.3797 = 10.239

   in 10.239 years the money will be 27 times

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