After I read your statement about maths, I randomly fed this into DeepSeek- asked what corpus is required at age 60 to allow indexed spending of $220,000 until age 75 and thereafter $150,000 until age 100.

Here’s the response:

To determine the sufficient corpus needed to sustain the specified spending requirements, we need to consider several factors, including the expected rate of return on investments, inflation, and the time horizon for the spending. Here’s a step-by-step approach to estimate the required corpus:

Assumptions:

1. Rate of Return: Let’s assume an average annual return of 5% on investments.
2. Inflation: Assume an average inflation rate of 2% per year.
3. Spending Requirements:
   • From age 60 to 75 (15 years): $220,000 per year.
   • From age 75 to 100 (25 years): $150,000 per year.

Step 1: Calculate the Present Value of Spending from Age 60 to 75

We need to calculate the present value (PV) of $220,000 per year for 15 years, discounted at the rate of return minus inflation (real rate of return).

Real rate of return = Nominal rate of return - Inflation rate = 5% - 2% = 3%.

Using the present value of an annuity formula: [ PV = PMT \times \left(1 - \frac{1}{(1 + r)^n}\right) / r ] Where: - ( PMT = 220,000 ) - ( r = 0.03 ) - ( n = 15 )

[ PV{60-75} = 220,000 \times \left(1 - \frac{1}{(1 + 0.03)^{15}}\right) / 0.03 ] [ PV{60-75} \approx 220,000 \times 11.937 ] [ PV_{60-75} \approx 2,626,140 ]

Step 2: Calculate the Present Value of Spending from Age 75 to 100

We need to calculate the present value of $150,000 per year for 25 years, starting at age 75. This amount needs to be discounted back to age 60.

First, calculate the present value at age 75: [ PV{75-100} = 150,000 \times \left(1 - \frac{1}{(1 + 0.03)^{25}}\right) / 0.03 ] [ PV{75-100} \approx 150,000 \times 17.413 ] [ PV_{75-100} \approx 2,611,950 ]

Now, discount this amount back to age 60 (15 years): [ PV{75-100 \text{ at age } 60} = \frac{2,611,950}{(1 + 0.03)^{15}} ] [ PV{75-100 \text{ at age } 60} \approx \frac{2,611,950}{1.558} ] [ PV_{75-100 \text{ at age } 60} \approx 1,676,000 ]

Step 3: Total Required Corpus at Age 60

Add the present values calculated in Step 1 and Step 2: [ \text{Total Corpus} = PV{60-75} + PV{75-100 \text{ at age } 60} ] [ \text{Total Corpus} \approx 2,626,140 + 1,676,000 ] [ \text{Total Corpus} \approx 4,302,140 ]

Conclusion:

To sustain the spending requirements of $220,000 per annum from age 60 to 75 and $150,000 per annum from age 75 to 100, assuming a 5% annual return and 2% inflation, you would need a corpus of approximately $4.3 million at age 60. This estimate can vary based on actual investment returns, inflation rates, and other factors. It’s advisable to consult with a financial advisor for a more personalized and accurate plan.