Subject
Quantitative Aptitude
Topic
Interest
What is the difference between the amount on Rs 10,000 after years at 4% per annum, compounded yearly and half yearly?
What is the difference between the amount on Rs 10,000 after years at 4% per annum, compounded yearly and half yearly?
ক)
Rs. 10.02খ)
Rs. 12.2গ)
Rs. 20.4ঘ)
Rs. 4.08ঙ)
None of theseExplanation
We know that Formula: 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. 4.08Related questions
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