Q. At what rate per annum will 32000 Rs. yield a compound interest of 5044 Rs. in 9 months interest being compounded quarterly ?
Answer: 20%
Notes: Let the rate of CI be R per cent per annum.
$latex \therefore CI = P\left [ \left ( 1+\frac{R}{100} \right )^{T} - 1 \right ]&s=1$
$latex => 5044 = 32000\left [ \left ( 1+\frac{R}{400} \right )^{3} - 1 \right ]&s=1$
[∵ Interest is compounded quarterly]
$latex => \frac{5044}{32000} = \left ( 1+\frac{R}{400} \right )^{3} - 1&s=1$
$latex => \left ( 1+\frac{R}{400} \right )^{3} - 1 = \frac{1261}{8000}&s=1$
$latex => \left ( 1+\frac{R}{400} \right )^{3} = 1+\frac{1261}{8000}&s=1$
$latex => \left ( 1+\frac{R}{400} \right )^{3} = \frac{9261}{8000} = \left ( \frac{21}{20} \right )^{3}&s=1$
$latex => 1+\frac{R}{400} = \frac{21}{20} => \frac{R}{400} = \frac{21}{20}-1&s=1$
$latex => \frac{R}{400} = \frac{1}{20}&s=1$
$latex => R = \frac{400}{20} = 20\%&s=1$
Hence option [A] is correct answer.