Question

A sum borrowed under compound interest doubles itself in 10 years. When will it become fourfold of itself at the same rate of interest?
1. 24 years
2. 15 years
3. 20 years
4. 40 years

Answer 1

Correct Answer - Option 3 : 20 years

Given : 

A sum double itself in 10 years

Formula used : 

\(Amount = P(1+R/100)^n\)

2P = P (1+r%/100) ¹⁰     eq 1

4P = P (1+r%/100)  ⁿ   eq 2

Divide wq 2 / 1

  \(\frac{4}{2} = \frac{{{{\left( {1 + r/100} \right)}^n}}}{{\begin{array}{*{20}{c}} {{{\left( {1 + \frac{r}{{100}}} \right)}^{10}}}\\ {} \end{array}}}\)

2 × (1 +r/100)¹⁰ = (1 +r/100)ⁿ

(1 +r/100)²⁰ = (1 +r/100)ⁿ

N = 20 years