A sum of money at compound interest becomes double of itself in 15 yrs. The rate of interest is

The correct option is C 4.7%

Let the principal be P

Amount in 15 years will be 2P

Let the rate of interest be R% per annum

$2P=P{(1+\frac{R}{100})}^{15}$

$2={(1+\frac{R}{100})}^{15}$

Applying logarithm on both sides

$\log 2=\log 15(1+\frac{R}{100})$

$0.693=\log 15(1+\frac{R}{100})$

$\log (1+\frac{R}{100})=\frac{0.693}{15}=0.0462$

$1+\frac{R}{100}=antilog\left(0.0462\right)$

$1+\frac{R}{100}=1.0473$

$\frac{R}{100}=1.0473-1=0.0473$

$R=0.0473\times 100=4.73$

Rate of interest is 4.7%