The average growth rate for a certain stock over the last 50 years is reported to 

be 14% compounded annually. If your grandmother had invested $400 in the 

stock 50 years ago, what would her investment be worth today?

To determine the value of your grandmother’s investment today, we can use the compound interest formula:

\[
A = P \times (1 + r)^n
\]

where:
- $ A $ is the amount after $ n $ years (the final value of the investment),
- $ P $ is the principal (initial investment),
- $ r $ is the annual growth rate (expressed as a decimal),
- $ n $ is the number of years.

### Given values:
- $ P = 400 $
- $ r = 0.14 $ (since 14% as a decimal is 0.14)
- $ n = 50 $

### Calculating $ A $:
Substitute the values:

\[
A = 400 \times (1 + 0.14)^{50}
\]

1. Calculate $ 1 + 0.14 = 1.14 $.
2. Raise $ 1.14 $ to the power of 50.
3. Multiply the result by 400.

Let's work through it.

#### Step 1: Calculate $ 1.14^{50} $:

\[
1.14^{50} \approx 267.8635
\]

#### Step 2: Multiply by the initial investment:

\[
A = 400 \times 267.8635 \approx 107,145.40
\]

### Conclusion:
The investment would be worth approximately **$107,145.40** today.

Would you like further details or have questions on this topic?

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Here are five related questions you might find helpful:

1. How would the investment value change if the growth rate was 10% instead of 14%?
2. How does the compounding period (annually, monthly, daily) affect investment outcomes?
3. What is the difference between compound interest and simple interest in long-term investments?
4. How do fluctuations in growth rate impact the stability of long-term investments?
5. How would the final amount differ if the investment were compounded quarterly instead of annually?

**Tip:** Compounding frequency has a significant impact on investment outcomes over time.

The average growth rate for a certain stock over the last 50 years is reported to be 14% compounded annually. If your grandmother had invested $400 in the stock 50 years ago, what would her investment be worth today?

Discover how a $400 investment made 50 years ago grows to over $107,145 with a 14% annual compound interest rate. This problem explores the compound interest formula, exponential growth, and key finance principles, ideal for Grades 10-12.

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