Question

A sum of money at compound interest (period = 1year) is doubled in 20 years. Then the number of years required to treble the sum will be

• A. 31.6 years
• B. 35 years
• C. 40 years
• D. 45 years

Answer 1

The correct option is A 31.6 years

The sum of money doubles itself in 20 years so we have

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

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

And let it treble itself in n years so we have,

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

now,

$(1+\frac{r}{100})=3^{\frac{1}{n}}$....................(3)

put 3 in 1 we get

$3^{\frac{20}{n}=2}$

Taking log on both sides

$\frac{20}{n}\log 3=\log 2$

$\frac{20}{n}=\frac{\log 2}{\log 3}$

$n=\frac{20\log 3}{\log 2}$

$n=31.6$

It will treble itself in $31.6$ years