Question
The compound interest on Rs 16000 for 9 months at 20% per annum, interest being compounded quarterly, is = ?
Answer: Option C
The interest is compounded quarterly,
$$\therefore R = \frac{{20}}{4} = 5\% $$
Time = 3 quarters
$$\eqalign{
& \therefore C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& = 16000\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& = 16000\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1} \right] \cr
& = 16000\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& = 16000 \times \frac{{1261}}{{8000}} \cr
& = {\text{Rs}}{\text{.}}\,\,2522 \cr} $$
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The interest is compounded quarterly,
$$\therefore R = \frac{{20}}{4} = 5\% $$
Time = 3 quarters
$$\eqalign{
& \therefore C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& = 16000\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& = 16000\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1} \right] \cr
& = 16000\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& = 16000 \times \frac{{1261}}{{8000}} \cr
& = {\text{Rs}}{\text{.}}\,\,2522 \cr} $$
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