a) Rs. 60000
b) Rs. 30000
c) Rs. 40000
d) Rs. 50000

Answer: d
Explanation: Rate of interest = 18%
Time = 2 year
When the interest is payable half yearly
Then, rate of interest = 9%
Time = 4 half – years
Let the principal be Rs. x
$$\eqalign{ & {\text{C}}{\text{.I}}{\text{. = }}x\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} – 1} \right]{\text{ }} \cr & = x\left[ {{{\left( {1 + \frac{9}{{100}}} \right)}^4} – 1} \right] \cr & = x\left[ {{{\left( {\frac{{109}}{{100}}} \right)}^4} – 1} \right] \cr & = x\left[ {1.4116 – 1} \right] \cr & = Rs.\,0.4116x \cr & {\text{According to question}} \cr & = x\left[ {{{\left( {1 + \frac{{18}}{{100}}} \right)}^2} – 1} \right] \cr & = x\left[ {{{\left( {\frac{{118}}{{100}}} \right)}^2} – 1} \right] \cr & = x\left[ {{{\left( {1.18} \right)}^2} – 1} \right] \cr & = x\left[ {1.3924 – 1} \right] \cr & = Rs.\,0.3924x \cr & {\text{According to question,}} \cr & 0.4116x – 0.3924x = 960 \cr & x = \frac{{960}}{{0.0192}} \cr & x = \frac{{960 \times 10000}}{{192}} \cr & x = 50000 \cr} $$