Question

find the amount on RS 256 in one year at 12 1/2 % per annum when the interest is compounded half yearly

Answer 1

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Answer 2

Answer:

$\red { Amount (A) }\green {= Rs \: 289 }$

Step-by-step explanation:

$Principal (P) = Rs\: 256$

$Rate \: of \: interest (r) =12 \frac{1}{2}\% \:per \:annum \\= \frac{25}{4} \%$

$Rate \: of \: half \: year = \frac{1}{2} \times \frac{25}{2} \\= \frac{25}{4}\%$

/* As Interest is compounded half yearly , so number of conversion periods in 1 years is 2

$n = 2$

$\boxed {\pink { Amount (A) = P\left( 1+ \frac{r}{100}\right)^{n} }}$

$= 256 \left( 1 + \frac{\frac{25}{4}}{100}\right)^{2}\\= 256 \left( 1 + \frac{25}{400}\right)^{2}\\= 256\left( 1 + \frac{1}{16}\right)^{2}\\= 256\left( \frac{16+1}{16}\right)^{2}\\= 256\left( \frac{17}{16}\right)^{2}\\=256\times \frac{17}{16} \times \frac{17}{16}\\= 256 \times \frac{289}{256} = Rs\:289$

Therefore.,

$\red { Amount (A) }\green {= Rs \: 289 }$

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