Correct Answer: 18 months

Solution : Given: The interest is being compounded half yearly and the rate of interest is 20 percent per annum.
Use the formula, $A=P[1+\frac{R}{n}]^{nt}$ where $A$, $P$, $R$, $n$, and $t$ are the amount, principal, rate, number of times interest applied per period and number of periods elapsed.
$19965=15000[1+\frac{20}{100\times 2}]^{2t}$
⇒ $\frac{19965}{15000}=[1+\frac{20}{100\times 2}]^{2t}$
⇒ $(\frac{11}{10})^3=[1+\frac{1}{10}]^{2t}$
⇒ $(\frac{11}{10})^3=(\frac{11}{10})^{2t}$
⇒ $2t=3$
⇒ $t=\frac{3}{2}$ years
⇒ $t=\frac{3}{2}\times 12=18$ months
Hence, the correct answer is 18 months.