Question

If A = Rs. 1000, n = 2 years, R = 6% p.a compound interest payable half-yearly then principal (P)

Answer 1

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

$\bold{\underline{Given,}}$

$\bold{Amount \: (A) = Rs \: \: 1000}$

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

$\bold{Rate \: (R) = 6\%}$

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

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

$\bold{W e \: \: know \: \: that}$

$\bold{Amount = P \times (1 + \frac{R}{200} ) {}^{2n}} \\ \\ \bold{= > 1000 = P \times (1 + \frac{6}{200} ) {}^{2 \times 2}} \\ \\ \bold{= > 1000 = P \times ( \frac{206}{200} ) {}^{4} }$

$\bold{= > 1000 = P \times \frac{206}{200} \times \frac{206}{200} \times \frac{206}{200} \times \frac{206}{200} }\\ \\\bold{ = > P = \frac{1000 \times 200 \times 200 \times 200 \times 200}{206 \times 206 \times 206 \times 206}} \\ \\ \bold{= > P = 888.48}$

$\bold{Hence, \: \: the \: \: principal \: \: is \: \: rs \: 888.48}$