Question

a certain sum of money double itself in 4 years at compound interest. In how many years it will become 32 times to itself..??
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Answer 1

Given:

A certain sum of money double itself in 4 years at compound interest.

To find:

In how many years it will become 32 times to itself?

Solution:

Let the prin cipal amount be x

$A = P(1+\frac{R}{100} )^{T}$

$2x = x(1+\frac{R}{100} )^{4}$

$2 = (1+\frac{R}{100} )^{4}$

$1+\frac{R}{100} = 2^{1/4}$

$32x = x(1+\frac{R}{100} )^{T}$

∵ $1+\frac{R}{100} = 2^{1/4}$

∴ $32 = 2^{T/4}$

$2^{5} = 2^{T/4 }$

5 = T/4

T = 5 × 4

T = 20 years

Therefore, in 20 years the principal amount will become 32 times of itself.