Question

Mr. X started a financial company, where a sum of money becomes 1728/1331 times when invested for three years in scheme where interest is compounded annually, how long will the same amount of money take to fourfold, if invested at the same rate of interest in a scheme where interest is computed using simple interest method?
1. 22 years
2. 33 years
3. 44 years
4. 25 years

Answer 1

Correct Answer - Option 2 : 33 years

Given∶

A sum of money becomes 1728/1331 times when invested for three years in scheme where interest is compounded annually.

Formula Used∶

A = P[ 1 +R/100]ⁿ

S.I. = PRT/100 

Calculation∶

We know that,

A = P[ 1 +R/100]ⁿ

So, amount becomes 1728/1331 times principal in 3 years

1728/1331 × P = P(1 + R/100)ⁿ

⇒ (12/11)³ = (1 + R/100)³

⇒ 12/11 = 1 + R/100

⇒ R/100 = 12/11 - 1 = 1/11

⇒ R = 100/11

In the case of simple interest the amount becomes four times(i.e.4 P)

A = P + SI

⇒ 4P = P + (P × R × T/100)

⇒ 3P = P × R × T/100

⇒ 3 × 100 = R × T

⇒ 300 = (100/11) × T

⇒ T = 11 × 3

⇒ 33

∴ If will take 33 years to make the money fourfold.