Question

If rs 16000amount to rs 23425.60 at 20%per annum compounded semi annually find the time period

Answer 1

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

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

$\bold{P = Rs \: \: 16000}$

$\bold{A = Rs \: \: 23425.60}$

$\bold{R = 20\% \: \: p.a.}$

$\bold\pink{Let \: \: the \: \: time \: \: be \: \: t \: \: years}$

$\bold\red{Since \: \: compounded \: \: semi \: annually}$

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

$\bold{Amount = P \times (1 + \frac{R}{200} ) {}^{2T}} \\ \\ \bold{= > 23425.60 = 16000 \times (1 + \frac{20}{200} ) {}^{2T} }\\ \\ \bold{= > \frac{2342560}{100 \times 16000} = ( \frac{220}{200} ) {}^{2T} }$

$\bold{ = > \frac{14641}{10000} = ( \frac{11}{10} ) {}^{2T}} \\ \\ \bold{= > ( \frac{11}{10} ) {}^{4} = ( \frac{11}{10} ) {}^{2T} }\\ \\ \bold{= > 2T= 4} \\ \\ \bold{= > T = \frac{4}{2} }\\ \\ = > \bold{T= 2}$

$\boxed{\boxed{\boxed{\bold{Hence, \: \: the \: \: time \: \: is \: \: 2 \: \: years.}}}}$

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