Suppose a man invested 

​$250250 

at the end of 1900 in each of three funds that tracked the averages of​ stocks, bonds, and​ cash, respectively. Assuming that these investments grew at the rates given in the accompanying​ table, approximately how much would each have been worth at the end of 

20192019​? 

​(Note: Assume the initial investments were the equivalent of 

​$250250 

in 

20192019 

​dollars.)

...

Question content area top right

Part 1

**Category**

**Average Annual Return**

Stocks

7.57.5​%

Bonds

1.81.8​%

Cash

0.60.6​%

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Part 1

His investment in the fund tracking stocks would be worth approximately 

​$

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.

Suppose a man invested $250 at the end of 1900 in each of three funds that tracked the averages of stocks, bonds, and cash, respectively. Assuming that these investments grew at the rates given in the accompanying table, approximately how much would each have been worth at the end of 2019? (Note: Assume the initial investments were the equivalent of $250 in 2019 dollars.)

Discover how a $250 investment in stocks, bonds, and cash in 1900 would grow by 2019 using compound interest. Learn how to apply the formula FV = P * (1 + r/100)^n with annual returns of 7.5% for stocks, 1.8% for bonds, and 0.6% for cash. Suitable for Grades 10-12 students.

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