Question

What sum invested for 1.5 years compounded half yearly at the rate of 8%p.a.,will amount to ₹17576

Answer 1

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

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

$\bold{A= Rs \: \: 17576}$

$\bold{T = 2 \: \: years}$

$\bold{R = 8\% \: \: p.a.}$

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

$\bold\blue{Since \: \: compounded \: \: half \: yearly}$

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

$\bold{Amount = P \times (1 + \frac{R}{200} ) {}^{2T}} \\ \\ \bold{ = > 17576 = P \times (1 + \frac{8}{200} ) {}^{2 \times 1.5} }\\ \\ \bold{= > 17576 = P \times ( \frac{208}{200} ) {}^{3} }\\ \\ \bold{ = > 17576 = P \times \frac{208}{200} \times \frac{208}{200} \times \frac{208}{200}}$

$\bold{ = > P = \frac{17576 \times 200 \times 200 \times 200}{208 \times 208 \times 208}} \\\\ \bold{= > P = Rs \: \: 15625 \: \:}$

$\bold\red{\boxed{Hence, \: \: the \: \: sum \: \: is \: \: Rs \: \: 15625.}}$
$\boxed{\boxed{\bold{\green{I \: \: hope \: \: it \: \: will \: \: help \: \: you}}}}$