To calculate the value of each investment at the end of 2019, we'll use the formula for compound interest, which takes into account the average annual return over the period.

1. Compound Interest Formula

The future value $FV$ of an investment is given by: $FV = P \times \left(1 + \frac{r}{100}\right)^n$ where:

• $P$ is the initial investment,
• $r$ is the average annual return (as a percentage),
• $n$ is the number of years the investment is held.

2. Calculate the Number of Years

The investment period from the end of 1900 to the end of 2019 is: $n = 2019 - 1900 = 119 \text{ years}$

3. Calculating the Future Value for Each Category

Stocks:

• Initial Investment: $250
• Annual Return: 7.5%

$FV_{\text{Stocks}} = 250 \times \left(1 + \frac{7.5}{100}\right)^{119} = 250 \times (1.075)^{119}$

Bonds:

• Initial Investment: $250
• Annual Return: 1.8%

$FV_{\text{Bonds}} = 250 \times \left(1 + \frac{1.8}{100}\right)^{119} = 250 \times (1.018)^{119}$

Cash:

• Initial Investment: $250
• Annual Return: 0.6%

$FV_{\text{Cash}} = 250 \times \left(1 + \frac{0.6}{100}\right)^{119} = 250 \times (1.006)^{119}$

4. Calculate the Values

Let's compute the future values for each of the investments:

Stocks:

$FV_{\text{Stocks}} \approx 250 \times (1.075)^{119} \approx 250 \times 5173.47 \approx 1,293,367.50$

Bonds:

$FV_{\text{Bonds}} \approx 250 \times (1.018)^{119} \approx 250 \times 898.73 \approx 224,682.50$

Cash:

$FV_{\text{Cash}} \approx 250 \times (1.006)^{119} \approx 250 \times 229.84 \approx 57,460.00$

Summary of Results:

• Stocks: Approximately $1,293,367.50
• Bonds: Approximately $224,682.50
• Cash: Approximately $57,460.00

Questions or further breakdown needed?

5 Related Questions:

1. How would the values change with different investment periods?
2. How does inflation impact these future values?
3. What if the returns were compounded quarterly instead of annually?
4. What would the values be if $500 had been invested instead?
5. How does diversification affect risk and return in such investments?

Tip: For long-term investments, small differences in the annual return significantly affect the final value.