Let's say I have 1 cr in my bank at the age of retirement which grows at 9% per year. My monthly expense at that time is 50000 which increase annually by 6% due to inflation.. how long will my funds last. Show a detailed calculation 

To determine how long your funds will last given your assumptions, we can approach this problem as follows:

### Problem Breakdown

1. **Initial Investment**: ₹1 crore (₹1,00,00,000)
2. **Growth Rate of Investment**: 9% per annum
3. **Initial Monthly Expense**: ₹50,000
4. **Expense Growth Rate (Inflation)**: 6% per annum

### Step-by-Step Calculation

1. **Annual Return on Investment**: Calculate the yearly growth of the investment at 9%.
2. **Annual Expenses**: Convert monthly expenses into annual expenses, and then increase them each year by 6%.
3. **Net Impact Each Year**: Deduct the annual expenses from the annual returns to see how the funds change each year.
4. **Termination Condition**: Continue until the funds are depleted.

### Detailed Calculation

Let's denote:

- \( I_0 \): Initial investment = ₹1,00,00,000
- \( r \): Annual return rate = 9%
- \( E_0 \): Initial annual expenses = 12 × ₹50,000 = ₹6,00,000
- \( i \): Annual expense growth rate (inflation) = 6%

We will calculate the balance at the end of each year, considering the growth of investment and the increasing expenses.

Let's compute this step-by-step.Your funds will last for **24 years** under the given conditions, and at the end of the 24th year, there will be approximately ₹18,67,861 left.

### Detailed Calculation Explanation

1. **Year 0 (Starting Point):**
   - Initial Investment: ₹1,00,00,000
   - Annual Expense: ₹6,00,000

2. **Year 1:**
   - Investment Growth: ₹1,00,00,000 × 9% = ₹9,00,000
   - Updated Investment: ₹1,00,00,000 + ₹9,00,000 - ₹6,00,000 = ₹1,03,00,000
   - Expense for Year 2: ₹6,00,000 × 1.06 = ₹6,36,000

This pattern continues each year with the investment growing by 9% and expenses increasing by 6%. By the 24th year, the funds are nearly depleted.

Would you like a more detailed year-by-year breakdown or have any other questions? Here are some related questions:

1. What would happen if the annual return rate changed to 8% or 10%?
2. How would changes in the inflation rate affect the duration?
3. What if you adjusted the initial withdrawal rate or added lump sums?
4. How would different investment strategies impact longevity?
5. What’s the impact of adjusting your monthly expenses periodically?

**Tip**: To extend the life of your funds, consider adjusting withdrawal rates or exploring alternative investments with potentially higher returns but manageable risk.

Learn how long your retirement funds will last with a detailed calculation involving compound interest growth and inflation-adjusted expenses. This problem covers key concepts in finance, including compound interest and inflation adjustments. Suitable for adult learners.

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