Question

The time required for a sum of money to double at $5$% annum compounded continuously is (in years)

• A. $13.9$
• B. $13$
• C. $13.5$
• D. $14.3$

Answer 1

Answer: (D)

Amount after $n$ years compounded annually$=P(1+\frac{r}{100}{)}^n$

Where, $P$ is the principal amount and $r$ is the interest rate per annum.

ie, $2P=P(1+\frac{r}{100}{)}^n\Rightarrow 2=(1+\frac{5}{100}{)}^n=(1+\frac{1}{20}{)}^n$

$\Rightarrow \ln 2=n\left(\ln \frac{21}{20}\right)\Rightarrow n=\frac{\ln 2}{\ln 21-\ln 20}\approx 14.3$

Option D is the correct answer.