**Directions:** Both Christina and Alizeh started by investing $10,000 and leaving it for 20 years. If the investment returns compound annually, solve for how much each of their investments are worth after 20 years. 





Question 4

Answer

Alizeh plans on leaving her $10,000 invested for 20 years. 

Write an equation representing her investment’s value, y, after x years. 

What is the value of Alizeh’s investment after 20 years?

To solve this, we'll use the formula for compound interest, which is:

\[
y = P \times (1 + r)^x
\]

where:
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate,
- $ x $ is the number of years,
- $ y $ is the value of the investment after $ x $ years.

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Let's go through each part:

### Part 1: Write an Equation Representing Alizeh’s Investment’s Value

Since we don't know the exact interest rate Alizeh is using, let’s write her investment's value as:

\[
y = 10000 \times (1 + r)^x
\]

where $ r $ represents the annual interest rate.

### Part 2: Calculate the Value of Alizeh’s Investment After 20 Years

To find the exact value of Alizeh’s investment after 20 years, we would need the specific value of $ r $ (the annual interest rate). 

If you provide the interest rate, I can compute the exact value of the investment after 20 years.

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Do you have the interest rate for Alizeh’s investment? Or would you like to proceed with a specific example? 

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### Related Questions

1. How does the compound interest formula differ if interest compounds quarterly instead of annually?
2. If Alizeh’s investment compounds semi-annually, how would that impact the growth over 20 years?
3. What would be the final investment value if she withdrew half of the amount after 10 years and reinvested the rest?
4. How would Christina’s investment value change if her interest rate is 1% higher than Alizeh’s?
5. How does simple interest differ from compound interest in long-term investment outcomes?

### Tip

In compound interest calculations, the frequency of compounding periods (annually, semi-annually, quarterly) significantly impacts the final investment value over time.

Both Christina and Alizeh started by investing $10,000 and leaving it for 20 years. If the investment returns compound annually, solve for how much each of their investments are worth after 20 years.

Write an equation representing Alizeh’s investment’s value, y, after x years. What is the value of Alizeh’s investment after 20 years?

Explore how to calculate compound interest for a $10,000 investment over 20 years, with a focus on the formula y = P * (1 + r)^x. Learn the impact of annual compounding and see how to determine the final investment value. This resource is ideal for high school students and financial learners.

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