What is the difference between the amount on Rs 10,000 after \(1\frac{1}{2}\) years at 4% per annum, compounded yearly and half yearly?
Solution
Correct Answer: Option D
We know that
Formula:
\(\Rightarrow {\text{Amount}} = \left[ {{\text{Principal}}\left\{ {{{\left( {1 + \frac{{{\text{rate}}}}{{100}}} \right)}^{time\ period}}} \right\}} \right]\)
Amount, when interest is compounded yearly:
\(\eqalign{ & {A_1} = \left[ {10,000 \times \left( {1 + \frac{4}{{100}}} \right) \times \left( {1 + \frac{{\frac{1}{2} \times 4}}{{100}}} \right)} \right]Rs \cr & \Rightarrow {A_1} = \left( {10,000 \times \frac{{26}}{{25}} \times \frac{{51}}{{50}}} \right)Rs \cr & \Rightarrow {A_1} = 10608\ Rs \cr}\)
Now amount, when interest is compounded half yearly:
∴ R = 2%
∴ n = 3
\(\eqalign{ & {A_2} = \left[ {10,000 \times {{\left( {1 + \frac{2}{{100}}} \right)}^3}} \right]Rs \cr & \Rightarrow {A_2} = \left( {10000 \times \frac{{51}}{{50}} \times \frac{{51}}{{50}} \times \frac{{51}}{{50}}} \right)Rs \cr & \Rightarrow {A_2} = 10612.08\ Rs \cr}\)
∴ Required difference = Rs (10612.08 – 10608.)
= Rs. 4.08
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