Question

Rajgiri advice his friend Prem to invest his money in Muthoot Finance Ltd, Prem invested certain sum of money at compound interest which doubles itself in 4 years, interest being payable annually. Find in how much time period will it be sixteen times?
1. 18 years
2. 12 years
3. 14 years
4. 16 years

Answer 1

Correct Answer - Option 4 : 16 years

Given∶

A certain sum of money compound interest which doubles itself in 4 years

Formula Used∶

A = P (1 + R/100)ⁿ

Calculation∶

Let the principal be Rs. P and rate f interest be R% p.a.

As the money doubles itself in 4 years, we have

2P = P (1 + R/100)⁴ 

⇒ (1 + R/100)⁴= 2P/P = 2

⇒ 1 +R/100 = 2^1/4

Let the money becomes 16 times in n years, then

16 P= P(1 + r/100)ⁿ

⇒ (1 + R/100)ⁿ = 16P/P = 16

⇒ (1 + R/100)ⁿ = (2)⁴

⇒ (2^1/4)ⁿ = 2⁴

⇒ n/4 = 4

⇒ n = 16

∴ The required time period is 16 years.