Question : In how many months will Rs. 8000 yield Rs. 2648 if compound interest at 20% per annum is compounded semi-annually?
Option 1: 18
Option 2: 24
Option 3: 12
Option 4: 30
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Correct Answer: 18
Solution : We have, $P$ = Rs. 8,000, $r$ = 20% and $t$ = 2 (compounded semi-annually). $A$ = $P$ + $\text{Interest}$ = Rs. 8000 + Rs. 2648 = Rs. 10,648. $A = P \left(1+\frac{\frac{r}{2}}{100}\right)^{2t}$ $⇒10648 = 8000 \left(1+\frac{\frac{20}{2}}{2}\right)^{2t}$ $⇒1.331 = \left(1.1\right)^{2t}$ $⇒(1.1)^3 = \left(1.1\right)^{2t}$ $⇒ 3 = 2t$ $⇒t=\frac{3}{2}$ or 18 months. Hence, the correct answer is 18.
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