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Question:

An amout of Rs. 10,000 becomes Rs. 14,641 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Explanation:

Let the interest rate be r% p.a.

If compounding is done n times in a year, the amount due after t years can be calclated as $\mathrm{P}\times {\left(1+\frac{\mathrm{r}/\mathrm{n}}{100}\right)}^{\mathrm{t}\times \mathrm{n}}$

Here, compounding in done 2 times in a year, hence n = 2.

⇒ 14641 = $10000\times {\left(1+\frac{\mathrm{r}/2}{100}\right)}^{2\times 2}$

⇒ 14641 = $10000\times {\left(1+\frac{\mathrm{r}/2}{100}\right)}^4$

⇒ 11⁴ = ${10}^4\times {\left(1+\frac{\mathrm{r}/2}{100}\right)}^4$

⇒ 11 = $10\times \left(1+\frac{\mathrm{r}/2}{100}\right)$

⇒ $\left(1+\frac{\mathrm{r}/2}{100}\right)$ = 1.1

⇒ r/2 = 10

⇒ r = 20%

Hence, option (c).