To solve this, we need to calculate the annual deposit Asif must make to accumulate Rs. 5,000,000 by the time he turns 40, assuming an interest rate of 11% per annum.

Step-by-Step Breakdown:

1. Future Value (FV) Formula: The future value of a series of annual deposits can be calculated using the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$ Where:

   • $FV = 5,000,000$ (target amount)
   • $P$ = annual deposit (what we are solving for)
   • $r = 11\% = 0.11$ (annual interest rate)
   • $n = 40 - 30 = 10$ years (number of deposits)

2. Rearranging the formula to solve for $P$: $P = \frac{FV \times r}{(1 + r)^n - 1}$ Substituting the values: $P = \frac{5,000,000 \times 0.11}{(1 + 0.11)^{10} - 1}$

3. Calculation:

   • First calculate $(1 + 0.11)^{10}$: $(1.11)^{10} = 2.853116$
   • Now, subtract 1: $2.853116 - 1 = 1.853116$
   • Now calculate $P$: $P = \frac{5,000,000 \times 0.11}{1.853116} = \frac{550,000}{1.853116} \approx 297,391.4$

Thus, the annual deposit required is approximately Rs. 299,007, which corresponds to option (b).

Final Answer: (b) Rs. 299,007

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Would you like further details on any part of the calculation? Here are some related questions that might interest you:

1. How does the interest rate affect the total amount of deposit needed?
2. What is the difference between a simple interest and compound interest calculation in this scenario?
3. How can changing the number of years (n) affect the annual deposit needed?
4. What are the implications of inflation when making such long-term investment decisions?
5. How can someone optimize this process with different compounding frequencies (quarterly, monthly, etc.)?

Tip: It's always a good idea to check the exact details of the compounding frequency when calculating future value, as it can drastically affect the outcome.