Question

A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 8 years. Find in how many years will the money becomes twenty-seven times of itself at the same rate of interest p.a.

Answer 1

Let principal = X, A = 3X, T = 8 years, R = ?

Case I,

`"A" = "P"[ 1 + "R"/100 ]^"T"`

`"3X" = "X"[ 1+ "R"/100 ]^8`

`3^(1/8) = 1 + "R"/100 `             ...(1)

Case II,

P = X, A = 27X, T = ?

`27"X" = "X"[ 1 + "R"/100 ]^"T"`

`27^(1/T) = 1 + "R"/100`          ...(2)

From (1) and (2)

`3^(1/8) = 27^(1/T)`

`3^(1/8) = 3^(1/8) = 3/"T"`

T = 24

Time = 24 years.