Calculate the interest on Amith's drawings at 12% p.a. for the year ending on 31.03.2024 under the product method.
Understand the Problem
The question is asking us to calculate the interest on Amith's drawings for a specific period at a 12% annual interest rate using the product method.
Answer
The total interest is $300$.
Answer for screen readers
The total interest on Amith's drawings for the year ending on 31.03.2024 is $300$.
Steps to Solve
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Understand the Drawings and Dates
Amith's drawings and the dates are:- Rs. 5,000 on 01.05.2023
- Rs. 6,000 on 30.10.2023
- Rs. 4,000 on 30.11.2023
- Rs. 6,000 on 01.01.2024
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Calculate the Time for Each Drawing
We'll calculate the time from each drawing date to the end date of 31.03.2024.- For Rs. 5,000: From 01.05.2023 to 31.03.2024 = 10 months
- For Rs. 6,000: From 30.10.2023 to 31.03.2024 = 5 months
- For Rs. 4,000: From 30.11.2023 to 31.03.2024 = 4 months
- For Rs. 6,000: From 01.01.2024 to 31.03.2024 = 3 months
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Convert Time into Years
Convert the months to years for the purpose of interest calculations:- 10 months = $\frac{10}{12}$ years
- 5 months = $\frac{5}{12}$ years
- 4 months = $\frac{4}{12}$ years
- 3 months = $\frac{3}{12}$ years
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Calculate Interest for Each Drawing
Use the formula for interest, $I = P \times R \times T$, where:-
(P) = Principal amount
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(R) = Rate of interest = 12% = 0.12
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(T) = Time in years
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For Rs. 5,000:
$$ I_1 = 5000 \times 0.12 \times \frac{10}{12} $$ -
For Rs. 6,000:
$$ I_2 = 6000 \times 0.12 \times \frac{5}{12} $$ -
For Rs. 4,000:
$$ I_3 = 4000 \times 0.12 \times \frac{4}{12} $$ -
For Rs. 6,000:
$$ I_4 = 6000 \times 0.12 \times \frac{3}{12} $$
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Sum Up the Interests
Finally, sum the interests calculated for all drawings:
$$ \text{Total Interest} = I_1 + I_2 + I_3 + I_4 $$
The total interest on Amith's drawings for the year ending on 31.03.2024 is $300$.
More Information
The calculation uses the product method to evaluate interest based on the varying duration of the drawings. This method efficiently determines interest for multiple transactions at different times.
Tips
- Not Converting Months to Years: Ensure that the time periods are converted accurately to years for the interest calculation.
- Incorrect Application of Interest Formula: Make sure you apply the interest formula correctly with appropriate values for (P), (R), and (T).