### Summary:

**Investing $100K in the S&P 500**in 1990, 1995, 2000, and 2010 would result in respective values of

**$2.29M, $1.28M, $456K, and $434K**by 2023, assuming no withdrawals.

**5% annually**would still leave substantial growth, with final values of

**$1.98M (1990), $1.02M (1995), $268K (2000), and $342K (2010)**by 2023.

To outline what happens if you invest $100,000 in the S&P 500 in 1990, 1995, 2000, and 2010, I will estimate the returns based on historical performance data for the S&P 500, assuming you reinvest all dividends and let the investment grow passively. Hereâ€™s a year-by-year overview:

**1. Investment in 1990:**

**Initial investment**: $100,000- The S&P 500 Index started around 353 points in 1990.
- As of 2023, the S&P 500 is around 4,500 points (varies by exact time), resulting in substantial growth.
**Annualized return**: The average return of the S&P 500 (including dividends) from 1990 to 2023 is around 10.5%.

Using a compound interest formula:

A=PÃ—(1+r)tA = P \times (1 + r)^tA=PÃ—(1+r)tWhere:

- AAA = final amount
- PPP = initial investment ($100,000)
- rrr = annualized return (10.5% or 0.105)
- ttt = number of years invested (1990â€“2023, or 33 years)

Plugging in the numbers:

A=100,000Ã—(1+0.105)33=100,000Ã—(1.105)33â‰ˆ2,293,000A = 100,000 \times (1 + 0.105)^{33} = 100,000 \times (1.105)^{33} \approx 2,293,000A=100,000Ã—(1+0.105)33=100,000Ã—(1.105)33â‰ˆ2,293,000So, a $100,000 investment in 1990 would grow to approximately **$2,293,000** by 2023.

**2. Investment in 1995:**

**Initial investment**: $100,000- The S&P 500 was around 470 points at the beginning of 1995.
**Annualized return**: The average return from 1995 to 2023 is also around 9.8%.

Using the compound interest formula for a 28-year period:

A=100,000Ã—(1+0.098)28â‰ˆ1,278,000A = 100,000 \times (1 + 0.098)^{28} \approx 1,278,000A=100,000Ã—(1+0.098)28â‰ˆ1,278,000A $100,000 investment in 1995 would grow to approximately **$1,278,000** by 2023.

**3. Investment in 2000:**

**Initial investment**: $100,000- The S&P 500 was around 1,400 points in early 2000.
- The S&P 500 experienced a downturn during the early 2000s dot-com bubble.
**Annualized return**: The average return from 2000 to 2023 is around 7%.

For a 23-year period:

A=100,000Ã—(1+0.07)23â‰ˆ456,000A = 100,000 \times (1 + 0.07)^{23} \approx 456,000A=100,000Ã—(1+0.07)23â‰ˆ456,000A $100,000 investment in 2000 would grow to approximately **$456,000** by 2023.

**4. Investment in 2010:**

**Initial investment**: $100,000- The S&P 500 was around 1,250 points at the start of 2010, following the 2008 financial crisis.
**Annualized return**: The average return from 2010 to 2023 is around 12.1%.

For a 13-year period:

A=100,000Ã—(1+0.121)13â‰ˆ434,000A = 100,000 \times (1 + 0.121)^{13} \approx 434,000A=100,000Ã—(1+0.121)13â‰ˆ434,000A $100,000 investment in 2010 would grow to approximately **$434,000** by 2023.

### Summary of Investments:

**Investment in 1990**: $2,293,000**Investment in 1995**: $1,278,000**Investment in 2000**: $456,000**Investment in 2010**: $434,000

Each investment benefits from the power of compounding over time, with the earliest investment seeing the most significant growth. Investing earlier gives the most substantial returns due to the extended time for compound growth.

## What would happen if you withdrew 5% every year to live on?

o calculate the impact of withdrawing 5% annually from your investments in the S&P 500 while allowing the rest to compound, weâ€™ll use a similar approach as before but account for the withdrawals.

### Assumptions:

- You invest $100,000 at the start.
- You withdraw 5% of the initial investment each year (i.e., $5,000 annually).
- The withdrawal is taken at the end of each year.
- The growth of the S&P 500 follows historical returns.
- We use the same annualized returns from the previous analysis for each period.

### Formula to Adjust for Withdrawals:

The formula for withdrawals is slightly more complex than simple compounding. It accounts for reducing the base investment each year:

A=PÃ—(1+r)tâˆ’WÃ—[(1+r)tâˆ’1r]A = P \times (1 + r)^t - W \times \left[\frac{(1 + r)^t - 1}{r}\right]A=PÃ—(1+r)tâˆ’WÃ—[r(1+r)tâˆ’1]Where:

- AAA = final amount after withdrawals
- PPP = initial investment ($100,000)
- rrr = annualized return (varies by investment year)
- ttt = number of years invested
- WWW = annual withdrawal ($5,000)

**1. Investment in 1990 with 5% Withdrawal:**

**Initial Investment**: $100,000**Annualized Return**: 10.5%**Withdrawal**: $5,000 per year**Period**: 33 years (1990â€“2023)

Using the formula above:

A=100,000Ã—(1.105)33âˆ’5,000Ã—[(1.105)33âˆ’10.105]A = 100,000 \times (1.105)^{33} - 5,000 \times \left[\frac{(1.105)^{33} - 1}{0.105}\right]A=100,000Ã—(1.105)33âˆ’5,000Ã—[0.105(1.105)33âˆ’1]This gives us:

Aâ‰ˆ2,293,000âˆ’5,000Ã—61.84â‰ˆ2,293,000âˆ’309,200=1,983,800A \approx 2,293,000 - 5,000 \times 61.84 \approx 2,293,000 - 309,200 = 1,983,800Aâ‰ˆ2,293,000âˆ’5,000Ã—61.84â‰ˆ2,293,000âˆ’309,200=1,983,800So, after 33 years with a 5% annual withdrawal, the investment would be worth approximately **$1,983,800** by 2023.

**2. Investment in 1995 with 5% Withdrawal:**

**Initial Investment**: $100,000**Annualized Return**: 9.8%**Withdrawal**: $5,000 per year**Period**: 28 years (1995â€“2023)

Using the formula:

A=100,000Ã—(1.098)28âˆ’5,000Ã—[(1.098)28âˆ’10.098]A = 100,000 \times (1.098)^{28} - 5,000 \times \left[\frac{(1.098)^{28} - 1}{0.098}\right]A=100,000Ã—(1.098)28âˆ’5,000Ã—[0.098(1.098)28âˆ’1]This gives us:

Aâ‰ˆ1,278,000âˆ’5,000Ã—50.75â‰ˆ1,278,000âˆ’253,750=1,024,250A \approx 1,278,000 - 5,000 \times 50.75 \approx 1,278,000 - 253,750 = 1,024,250Aâ‰ˆ1,278,000âˆ’5,000Ã—50.75â‰ˆ1,278,000âˆ’253,750=1,024,250So, after 28 years with a 5% withdrawal, the investment would be worth approximately **$1,024,250** by 2023.

**3. Investment in 2000 with 5% Withdrawal:**

**Initial Investment**: $100,000**Annualized Return**: 7%**Withdrawal**: $5,000 per year**Period**: 23 years (2000â€“2023)

Using the formula:

A=100,000Ã—(1.07)23âˆ’5,000Ã—[(1.07)23âˆ’10.07]A = 100,000 \times (1.07)^{23} - 5,000 \times \left[\frac{(1.07)^{23} - 1}{0.07}\right]A=100,000Ã—(1.07)23âˆ’5,000Ã—[0.07(1.07)23âˆ’1]This gives us:

Aâ‰ˆ456,000âˆ’5,000Ã—37.45â‰ˆ456,000âˆ’187,250=268,750A \approx 456,000 - 5,000 \times 37.45 \approx 456,000 - 187,250 = 268,750Aâ‰ˆ456,000âˆ’5,000Ã—37.45â‰ˆ456,000âˆ’187,250=268,750So, after 23 years with a 5% withdrawal, the investment would be worth approximately **$268,750** by 2023.

**4. Investment in 2010 with 5% Withdrawal:**

**Initial Investment**: $100,000**Annualized Return**: 12.1%**Withdrawal**: $5,000 per year**Period**: 13 years (2010â€“2023)

Using the formula:

A=100,000Ã—(1.121)13âˆ’5,000Ã—[(1.121)13âˆ’10.121]A = 100,000 \times (1.121)^{13} - 5,000 \times \left[\frac{(1.121)^{13} - 1}{0.121}\right]A=100,000Ã—(1.121)13âˆ’5,000Ã—[0.121(1.121)13âˆ’1]This gives us:

Aâ‰ˆ434,000âˆ’5,000Ã—18.33â‰ˆ434,000âˆ’91,650=342,350A \approx 434,000 - 5,000 \times 18.33 \approx 434,000 - 91,650 = 342,350Aâ‰ˆ434,000âˆ’5,000Ã—18.33â‰ˆ434,000âˆ’91,650=342,350So, after 13 years with a 5% withdrawal, the investment would be worth approximately **$342,350** by 2023.

**Summary of Investments with 5% Annual Withdrawals:**

**Investment in 1990**: Final balance =**$1,983,800****Investment in 1995**: Final balance =**$1,024,250****Investment in 2000**: Final balance =**$268,750****Investment in 2010**: Final balance =**$342,350**

### Insights:

- Withdrawing 5% annually still leaves substantial growth, especially with longer investment periods.
- The earlier the investment, the more substantial the final balance, even after consistent withdrawals.