Question

How much will Rs 2560 amount in one year at 12 1/2% p. a. When the interest is compounded half yearly.

Answer 1

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

$\bold{Given,}$

$\bold{Amount \: (A) = Rs \: \: 2560}$

$\bold{Time \: (T) = 1 \: \: year}$

$\bold{Rate \: (R) = 12 \frac{1}{2} \% = \frac{25}{2} \% \: p.a.}$

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

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

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

$\bold{A = P \times (1 + \frac{R}{200} ) {}^{2T} }\\ \\ \bold{= > 1560 = P \times (1 + \frac{25}{2 \times 200} ) {}^{2 \times 1} }\\ \\ \bold{= > 1560 = P \times (1 + \frac{1}{16} ) {}^{2}}$

$\bold{ = > 1560 = P \times \frac{17}{16} \times \frac{17}{16}} \\ \\\bold{ = > P = \frac{1560 \times 16 \times 16}{17 \times 17}} \\ \\ \bold{= > P = Rs \: \: 1381.86}$

$\bold{Hence, \: \: the \: \: sum \: \: is \: \: Rs \: \: 1381.86.}$