Question

a certain sum amounts to rest 297 0.25 in 2 years at 9% per annum compounded annually find the sum

Answer 1

$\boxed{\boxed{\boxed{\bold{\green{Solution :\longrightarrow }}}}}$

$\boxed{\boxed{\boxed{\bold{\red{Given,}}}}}$

$\bold{Amount \: (A) = Rs \: \: 2970.25}$

$\bold{Time \: (T) = 2 \: \: years}$

$\bold{Rate \: (R) = 9\% \: \: p.a.}$

$\bold\blue{Let \: \: the \: \: sum \: \: be \: \: Rs \: \: P.}$

$\bold\pink{Since \: \: compounded \: \: annually}$

$\bold\purple{We \: \: know \: \: that}$

$\bold{Amount = P \times (1 + \frac{R}{100} ) {}^{T}} \\ \\ \bold{= > 2970.25 = P \times (1 + \frac{9}{100} ) {}^{2} }$

$\bold{ = > 2970.25 = P \times \frac{109}{100} \times \frac{109}{100}} \\ \\ \bold{= > P = \frac{2970.25 \times 100 \times 100}{109 \times 109} }\\ \\ \bold{= > P = 0.25 \times 100 \times 100} \\ \\ \bold{= > P = Rs\: \: 2500}$

$\boxed{\boxed{\boxed{\bold{\red{Hence, \: \: the \: \: sum \: \: is \: \: Rs \: \: 2500.}}}}}$

$\boxed{\boxed{\boxed{\mathfrak{\green{I \: \: hope \: \: it \: \: will \: \: help \: \: you}}}}}$