A sum becomes 8 times of itself in 7 years at the rate of…

A sum becomes 8 times of itself in 7 years at the rate of compound interest (interest is compounded annually). In how many years will the sum becomes 4096 times of itself?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 28.

Understanding/Application

Let principal, rate and time be p, r and t respectively.

Amount after 7 years = 8p

A = p{1 + (r/100)}^t

ATQ -

p{1 + (r/100)}⁷ = 8p

{1 + (r/100)} = 8^1/7 ....(1

Let Amount after T years be 4096p.

p{1 + (r/100)}^T = 4096p

{1 + (r/100)}^T= 4096

Substituting (1 in above equation -

(8^1/7)^T = 4096

8^T/7 = 8⁴

On comparing -

T/7 = 4

T = 28 years

SSC GD 2019 PYQ — Question 73