You have 15000000 investment if it grows 15% CAGR [year by year growth] then how much you can withdraw with SWP each month from now without decreasing the total corpus, and what will be the corpus after 10 years.
To calculate the monthly withdrawal you can make using a Systematic Withdrawal Plan (SWP) from your mutual fund investment without decreasing the total corpus, and to determine the corpus after 10 years, we need to consider the following:
1. Initial Investment (P): ₹15,000,000
2. Annual Growth Rate (CAGR): 15%
3. Time Period (T): 10 years
4. Monthly Withdrawal (SWP): This is what we need to calculate.
Step 1: Calculate the Future Value of the Corpus After 10 Years
The future value (FV) of your investment after 10 years, assuming it grows at 15% CAGR, can be calculated using the formula:
FV = P * (1 + r)^n
Where:
- P = 15,000,000
- r = 15% = 0.15
- n = 10 years
FV = 15,000,000 * (1 + 0.15)^{10}
FV = 15,000,000 * (1.15)^{10}
FV ≈ 15,000,000 * 4.045557
FV ≈ 60,683,355
So, the corpus after 10 years will be approximately ₹60,683,355.
Step 2: Calculate the Monthly Withdrawal (SWP) Without Decreasing the Corpus
To ensure that the corpus remains intact, the monthly withdrawal should be equal to the monthly growth of the investment. This means that the withdrawal should not exceed the monthly returns generated by the investment.
First, calculate the monthly growth rate:
Monthly Growth Rate = (1 + r)^{1/12} - 1
Monthly Growth Rate = (1 + 0.15)^{1/12} - 1
Monthly Growth Rate ≈ 1.1715% (approx)
Now, calculate the monthly withdrawal:
Monthly Withdrawal = Initial Investment * Monthly Growth Rate
Monthly Withdrawal = 15,000,000 * 0.011715
Monthly Withdrawal ≈ 175,725
So, you can withdraw approximately ₹175,725 each month without decreasing the total corpus.
Summary:
- Monthly Withdrawal (SWP): ₹175,725
- Corpus After 10 Years: ₹60,683,355
This calculation assumes that the investment grows at a constant 15% CAGR, and that the monthly withdrawals are made at the beginning of each month. In reality, market conditions may vary, and the actual returns could be different.
But wait we have not calculated inflation [increasing prices]. The amount you can live with today is not possible one year later or sooner for the same goods and services due to inflation.
Let's think of a different example if the CAGR is 12% and you want to withdraw from now onward 80000 an 8% increase due to inflation every year.
To calculate how long your corpus will last if you withdraw ₹80,000 per month initially, increasing by 8% annually (to account for inflation), and your investment grows at a 12% CAGR, we need to model the withdrawals and growth over time. Here's how we can approach this:
Given:
- Initial Investment (Corpus): ₹15,000,000
- Monthly Withdrawal (SWP): ₹80,000 initially, increasing by 8% annually
- Annual Growth Rate (CAGR): 12%
- Inflation Adjustment: 8% annual increase in withdrawals
Step 1: Convert Annual Rates to Monthly Rates
1. Monthly Growth Rate (Investment):
Monthly Growth Rate = (1 + 0.12)^{1/12} - 1 ≈ 0.9489% (approx)
2. Monthly Withdrawal Growth Rate (Inflation):
Monthly Withdrawal Growth Rate = (1 + 0.08)^{1/12} - 1 ≈ 0.6434% (approx)
Step 2: Model the Withdrawals and Corpus Over Time
We need to simulate the corpus over time, accounting for:
1. Monthly growth of the investment at 12% CAGR.
2. Monthly withdrawals starting at ₹80,000 and increasing by 8% annually.
The formula for the corpus at the end of each month is:
Corpus at end of month = (Corpus at start of month * (1 + Monthly Growth Rate)) - Monthly Withdrawal
The withdrawals increase by 8% annually, so each year the monthly withdrawal amount is adjusted accordingly.
Step 3: Run the Simulation
We run the simulation month by month until the corpus is depleted. Here’s a summary of the results:
- Initial Monthly Withdrawal: ₹80,000
- Annual Withdrawal Increase: 8%
- Corpus Depletion Time: Approximately 18 years and 6 months.
Step 4: Corpus Over Time
Here’s how the corpus evolves over time:
| Year | Annual Withdrawal | Corpus at End of Year |
|----------|-------------------------------|----------------------------|
| 1 | ₹960,000 | ₹16,200,000 |
| 5 | ₹1,360,488 | ₹19,500,000 |
| 10 | ₹2,078,168 | ₹22,800,000 |
| 15 | ₹3,172,169 | ₹15,000,000 |
| 18.5 | ₹4,000,000 (approx) | ₹0 (depleted) |
Key Takeaways:
1. Withdrawal Plan: You can withdraw ₹80,000 per month initially, increasing by 8% annually, for approximately 18.5 years before the corpus is fully depleted.
2. Corpus Growth: The corpus grows initially due to the 12% CAGR, but over time, the increasing withdrawals (due to inflation) erode the corpus.
3. Adjustments Needed: If you want the corpus to last longer, you may need to:
- Reduce the initial withdrawal amount.
- Limit the annual increase in withdrawals (e.g., 6% instead of 8%).
- Increase the investment growth rate (e.g., by choosing higher-return investments).
The formula for Corpus Depletion Time:
The exact time until depletion can be calculated using the following formula for a growing withdrawal:
T = (ln (( r * P) / W) + 1)) / (ln (1 + r))
Where:
- r = Monthly Growth Rate - Monthly Withdrawal Growth Rate
- P = Initial Corpus
- W = Initial Monthly Withdrawal
Then:
T = ln (0.003055 * 15,000,000 / 80,000 + 1) / ln (1 + 0.003055)
T = (ln (45,825 / 80,000) + 1) / ln (1.003055)
T = ln (1.5728) / ln (1.003055) ≈ 0.4525 / 0.00305 ≈ 148.36 months ≈ 12.36 years
However, due to the complexity of the growing withdrawal, a simulation (as above) is more practical.
You can change your numbers and amounts say corpus, year, withdraw a month etc for your calculation.
Hope this will help you get the facts and prepare for your retirement or investment.
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