A man deposits rs 1000 in his Savings Account of a bank on the first Day of each months. Find tha interest earned by him at the end of 6 months at 8% Simple Interest.​

To find the interest earned by a man who deposits ₹1000 at the beginning of each month for 6 months in a Savings Account at 8% Simple Interest, we need to calculate the interest for each deposit individually because the deposits are made at different times.

### Step-by-Step Calculation:

1. **Formula for Simple Interest**:
   \[
   \text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
   \]
   Where:
   - \( P \) is the principal amount (₹1000 for each month),
   - \( R \) is the rate of interest (8% per annum),
   - \( T \) is the time period in years.

2. **Interest for each deposit**:
   Since the deposits are made at different times, the time period \( T \) for each deposit will be different.

   - For the deposit made in the 1st month, the time \( T \) is 6 months or \( \frac{6}{12} = 0.5 \) years.
   - For the deposit made in the 2nd month, the time \( T \) is 5 months or \( \frac{5}{12} \) years.
   - For the deposit made in the 3rd month, the time \( T \) is 4 months or \( \frac{4}{12} \) years.
   - For the deposit made in the 4th month, the time \( T \) is 3 months or \( \frac{3}{12} \) years.
   - For the deposit made in the 5th month, the time \( T \) is 2 months or \( \frac{2}{12} \) years.
   - For the deposit made in the 6th month, the time \( T \) is 1 month or \( \frac{1}{12} \) years.

3. **Interest calculation**:
   - **1st deposit**: \( SI_1 = \frac{1000 \times 8 \times 0.5}{100} = ₹40 \)
   - **2nd deposit**: \( SI_2 = \frac{1000 \times 8 \times \frac{5}{12}}{100} = ₹33.33 \)
   - **3rd deposit**: \( SI_3 = \frac{1000 \times 8 \times \frac{4}{12}}{100} = ₹26.67 \)
   - **4th deposit**: \( SI_4 = \frac{1000 \times 8 \times \frac{3}{12}}{100} = ₹20 \)
   - **5th deposit**: \( SI_5 = \frac{1000 \times 8 \times \frac{2}{12}}{100} = ₹13.33 \)
   - **6th deposit**: \( SI_6 = \frac{1000 \times 8 \times \frac{1}{12}}{100} = ₹6.67 \)

4. **Total Interest**:
   The total interest earned after 6 months is the sum of the interest for all deposits:
   \[
   \text{Total Interest} = 40 + 33.33 + 26.67 + 20 + 13.33 + 6.67 = ₹140
   \]

### Conclusion:
The man will earn a total of ₹140 in interest at the end of 6 months at 8% Simple Interest.

Would you like further details or explanations?

Here are 5 related questions:
1. How would the calculation change if the interest rate was compounded monthly?
2. What if the deposits were made at the end of each month instead of the beginning?
3. How would the interest earned change if the period was extended to 12 months?
4. What happens to the interest calculation if the rate increases to 10%?
5. How is simple interest different from compound interest?

**Tip**: Always ensure you understand whether interest is calculated on the basis of the deposit date (beginning vs. end of the month).

A man deposits ₹1000 in his Savings Account of a bank on the first day of each month. Find the interest earned by him at the end of 6 months at 8% Simple Interest.

Learn how to calculate the simple interest earned on monthly deposits of ₹1000 for 6 months at 8% interest. This step-by-step guide covers the basic concepts of simple interest, time periods, and interest rate calculations. Ideal for students in Grades 9-10.

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