In how many years will a sum of ₹ 800 at 10\% per annum compounded semi-annually become ₹ 926.10?
(a)$1 \frac{1}{3}$ years
(b)$1 \frac{1}{2}$ years
(c)$2 \frac{1}{3}$ years
(d)$2 \frac{1}{2}$ years
Answer
Answer (as printed): B
Explanation
Let the time be $n$ years. Then, $800 \times\left(1+\frac{5}{100}\right)^{2 n}=926.10$ or $\left(1+\frac{5}{100}\right)^{2 n}=\frac{9261}{8000}$ or $\left(\frac{21}{20}\right)^{2 n}=\left(\frac{21}{20}\right)^{3}$ or $2 n=3$ or $n=\frac{3}{2}$. $$\therefore n=1 \frac{1}{2} \text { years. }$$
Explanation as extracted from the printed page; notation may be imperfect.