Question

A sum of money at compound interest is doubled in $20$ years. Then the number of years required to tripple itself are

• A. $32$ years
• B. $35$ years
• C. $40$years
• D. $45$ years

Answer 1

The correct option is A $32$ years

We know that

$A=P{(1+\frac{r}{100})}^T$

According to the question,

$2P=P{(1+\frac{r}{100})}^{20}$

$2={(1+\frac{r}{100})}^{20}$ $.............\left(1\right)$

And

$3P=P{(1+\frac{r}{100})}^T$

$3={(1+\frac{r}{100})}^T$ $...........\left(2\right)$

From equation (1) and (2), we get

$3^{1/T}=2^{1/20}$

On taking $log$ both sides, we get

$\frac{1}{T}\log 3=\frac{1}{20}\log 2$

$T=\frac{20log3}{\log 2}$

$T=31.7$

$T\approx 32years$

Hence, this is the answer.