Question

In what time will a sum of money double itself at 15% p.a​

Answer 1

Given

Principal = P

Amount = w/o

rate = 15% per annum

time = t

___________________________

Solution

$\sf \color{red}\dfrac{compound \: interest}{a \: = 1(1 + \dfrac{r}{10} {)}^{t} }$

$\bf \implies \: 2p = p(1 + {\frac{15}{100})}^{t}$

$\implies \bf \dfrac{2p}{p} = (1 + {\dfrac{15}{100})}^{t}$

$\implies \bf \: 2 = ( {\dfrac{115}{100})}^{t}$

$\implies \bf \: { (\dfrac{23}{20} }^{t} )$

$\sf \color{red} \: method \: changed$

$\implies \bf \dfrac{2p}{p} = 1 + \dfrac{15t}{100}$

$\bf \implies \: 2 = 1 + \dfrac{15t}{100}$

$\implies \bf \dfrac{15t}{10} = 1$

$\bf \implies \: t = \dfrac{100}{15} = \dfrac{20}{3}$

$\bf \color{purple} \dfrac{simple \: interest}{a = 2p}$

$\bf \: si = a - principal \: amount$

$\bf \implies \: 2p - p = p$

$\color{pink} \bf \: si \: = \dfrac{p \times r \times t}{100}$

$\bf \implies \: \cancel{p} = \dfrac{ \cancel{p} \times 15 \times t}{100}$

$\bf \: \implies \: t = \dfrac{100}{15} = \dfrac{20}{3}$

____________________________

Note !!

Formula Which we Used are colored !

Answer 2

Answer:

$\huge\underline\mathfrak\red{❥Answer}$

Step-by-step explanation:

If the principal be x, then amount = 2x We know that, SI = Amount - Principal = 2x - x = x

$time = \frac{si \times 100}{principal \times rate} = \frac{ x \times 100}{x \times 15} \\ = \frac{20}{3 } = 6 \times \frac{2}{3} years$