Question

the compound interest on 1800 for 2 years is 378.The rate is?​

Answer 1

$\bf{\dag}\:\underline{\frak{Corrected\; Question :}}$

At what rate does the compound interest for rupees 1800 be rupees 378 in 2 years. If interest has been calculated annually?

$\rule{300}2$

According to the question,

$\sf Given\begin {cases}\sf { principal \implies1800 \: rs } \\ \sf{ time \implies} {2 \: year}\\ \sf \: c.i. \implies \: 378 \: rs\end {cases}$

✧ To Find ✧

• The rate = ?

$\implies \sf c.i. =p { ((1 + \frac{r}{100} )}^{t} - 1) \\ \\ \implies \sf \: \therefore \: 378 = 1800( {(1 + \frac{r}{100} )}^{2} - 1)$

Full solution

$\implies \boxed{\sf{\gray{ \frac{378}{1000} = (1 + \frac{r}{100})^{2} - 1 }}}$

$\implies\boxed{\sf{\gray{ \frac{378}{1800 + 1} = (1 + \frac{r}{100}) ^{2} }}}$

$\implies\boxed{\sf{\gray{ \frac{378 + 1800}{1800} = {(1 + \frac{r}{100} )}^{2} }}}$

$\implies\;\boxed{\sf{\gray{ \frac{2178}{1800} = {(1 + \frac{r}{100} )}^{2} }}}$

$\implies \: \boxed{\sf{\gray{ {( \frac{33}{30} )}^{2} = (1 + \frac{r}{100})^{2} }}}$

$\implies \boxed{\sf{\gray{ \frac{33}{30} = 1 + \frac{r}{100} }}}$

$\implies\boxed{\sf{\gray{ \frac{33}{30} - 1 = \frac{r}{100} }}}$

$\implies\boxed{\sf{\gray{ \frac{33 - 30}{30} = \frac{r}{100} }}}$

$\implies\boxed{\sf{\gray{ \frac{3}{30} = \frac{r}{100} }}}$

$\implies\therefore \boxed{\sf{\red{r = \frac{3}{30} \times 100 = 10\%}}}$

So the rate is 10%