Question

In \(3{{1} \over 3}\) years, a sum of money placed at compound interest doubles itself. Find the time in which it will become 8 times.
1. 5(1/3) years
2. 10 years
3. 12 years
4. 8 years

Answer 1

Correct Answer - Option 2 : 10 years

Given:

Time (n') = \(3{{1} \over 3}\) = (10/3) years

Formula used:

A = P(1 + R/100)n

Where A → amount

P → principal

R → rate 

n → time

Calculations:

Let the principal be Rs. P, the rate be R% p.a.

And the time in which it will become 8 times be n years.

According to the question,

⇒ 2P = P(1 + R/100)^10/3

⇒ 2 = (1 + R/100)10/3

⇒ 8 = (1 + R/100)10       ----(i)

And 8P = P(1 + R/100)ⁿ

⇒ 8 = (1 + R/100)n      ----(ii)

From (i) and (ii), we get

(1 + R/100)ⁿ = (1 + R/100)10

⇒ n = 10 years.

∴ The time in which it will become 8 times is 10 years.