Question

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is

• A. 2 Years
• B. 3 Years
• C. 4 Years
• D. 5 Years

Answer 1

The correct option is C

4 Years

Let "n" be the number of complete years takes for the given condition and P be the sum of money initially.
Sum of money after n years $P{(1+\frac{20}{100})}^n$
We have to find "n" such that sum of money after "n" years will be double of the initial sum of money
$\Rightarrow P{(1+\frac{20}{100})}^n\ge 2P$
$\Rightarrow P(1.2{)}^n\ge 2P$
Since number of complete years is asked in the question, n will be a whole number
$\Rightarrow$ We have to find the value of n such that $(1.2{)}^n\ge 2$
Put n = 2, $\Rightarrow {1.2}^2$ = 1.44, which is not greater than 2
Put n = 3, $\Rightarrow {1.2}^3$ = 1.728, which is not greater than 2
Put n = 4, $\Rightarrow {1.2}^4$ = 2.0736, which is greater than 2
So, the required number of complete years is 4 years.