Question

Calculate the compound interest on 10,000 for 2 1/2 year at the rate of 10% per annum compounded and annually

Answer 1

$Principal (P) = Rs \:10000</p><p>$

$Time (T) = 2 \frac{1}{2} \: years$

$Rate \:of \: interest (r) = 10\% \: per \: annum$

• First we have to find amount for 2 years:

$P = Rs \: 10000 \\T = 2 \: years \\r = 10\% \:p.a \\Conversion \: period (n) = 2$

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

$A = 10000\big( 1 + \frac{2}{100}\big)^{2}\\= 10000\big( 1 + 0.02\big)^{2} \\= 10000 \times (1.02)^{2} \\= 10000 \times 1.02 \times 1.02 \\= Rs\:10404$

$Compound \: Interest = Amount - P\\= 10404 - 10000\\= Rs \: 404 \: ---(1)$

• Interest for remaining 6 months :

$P = Rs \:10404 \\R = 10\%$

$T = 6 \:months = \frac{1}{2} \:year$

$Let \: Simple \:interest = I$

$\boxed { \pink { I = \frac{PTR}{100} }}$

$I = \frac{ 10404 \times \frac{1}{2} \times 10}{100}\\= Rs\:520.20\: ---(2)$

Therefore.,

$\red { Compound \: Interest } \\= (1) + (2) \\= Rs \:404 + Rs \:520.20\\=\green { Rs\:924.20}$

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