# 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?

2
by anshkhanna786

2015-04-06T00:09:40+05:30
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
2015-04-06T11:43:40+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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