a) Rs. 4500
b) Rs. 5000
c) Rs. 5500
d) Rs. 6000
Answer: b
Explanation:
$$\eqalign{
& {\text{Let the sum Rs}}{\text{. }}x{\text{ }} \cr
& {\text{C}}{\text{.I}}{\text{. when compounded half yearly}} {\text{ = Rs}}{\text{.}}\left[ {x \times {{\left( {1 + \frac{3}{{100}}} \right)}^2} – x} \right] \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{10609}}{{10000}}x – x} \right) \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{609x}}{{10000}}} \right) \cr
& {\text{C}}{\text{.I}}{\text{. when compounded yearly}} {\text{ = Rs}}{\text{.}}\left[ {x \times \left( {1 + \frac{4}{{100}}} \right) – x} \right] \cr
& = {\text{Rs}}{\text{.}}\left( {\frac{{26x}}{{25}} – x} \right) \cr
& = {\text{Rs}}{\text{.}}\frac{x}{{25}} \cr
& \therefore \frac{{609x}}{{10000}} – \frac{x}{{25}} = 104.50 \cr
& \frac{{209x}}{{10000}} = 104.50 \cr
& x = \left( {\frac{{104.50 \times 10000}}{{209}}} \right) \cr
& x = 5000 \cr} $$
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