Calculate the interest on Amith's drawings at 12% p.a. for the year ending on 31.03.2024 under the product method.

Steps to Solve

1. 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

2. 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

3. 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

4. Calculate Interest for Each Drawing
   Use the formula for interest, $I = P \times R \times T$, where:

   • (P) = Principal amount

   • (R) = Rate of interest = 12% = 0.12

   • (T) = Time in years

   • 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:
     $$ I_4 = 6000 \times 0.12 \times \frac{3}{12} $$

5. Sum Up the Interests
   Finally, sum the interests calculated for all drawings:
   $$ \text{Total Interest} = I_1 + I_2 + I_3 + I_4 $$