Question

At what rate per cent compound interest, does a sum of money becomes 1.44 times of itself in 2 years?​

Answer 1

•••●Solution●•••

Let P=x

A= 1.44 of P=1.44x

Time= 2 years

$\sf \: A = p(1 + \frac{r}{100} {)}^{2}$

$\rightarrow \sf1.44x = x(1 + \frac{r}{100} {)}^{2} \\ \\ \rightarrow \sf \frac{144 \cancel{x}}{100 \cancel{x} } = x(1 + \frac{r}{100} {)}^{2}$

$\rightarrow \sf( \frac{12}{10} {)}^{ \cancel2} = (1 + \frac{r}{100} {)}^{ \cancel2}$

$\rightarrow \sf \frac{12}{10} - 1 = \frac{r}{100} \\ \\ \rightarrow \sf \frac{2}{10} = \frac{r}{100} \\ \\ \implies\sf r =100 \times \frac{2}{10} = 20\%$

Hope it helps you....