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The image shows a math problem related to compound interest. Here's a breakdown of the question:

1. **Initial Deposit (P):** $2000
2. **Interest Rate (r):** 5.5% per year (compounded annually)
3. **Time (t):** The equation should predict the amount in any year past 2020.
4. **Formula:** You need to create an equation for compound interest in the form $ A(t) = P \left( 1 + \frac{r}{100} \right)^t $, where:
   - $ A(t) $ is the amount after time $ t $,
   - $ P $ is the initial principal ($2000),
   - $ r $ is the annual interest rate (5.5%), and
   - $ t $ is the number of years since 2020.

### (a) Equation for the Account
Using the formula $ A(t) = P \left( 1 + \frac{r}{100} \right)^t $:
- $ P = 2000 $
- $ r = 5.5 $

The equation becomes:
\[
A(t) = 2000 \left( 1 + \frac{5.5}{100} \right)^t = 2000 \left( 1.055 \right)^t
\]
This is the equation that predicts the amount in the account after $ t $ years.

### (b) Amount in 2050
- From 2020 to 2050, the time $ t $ is 30 years.
- Use the equation $ A(30) = 2000 \left( 1.055 \right)^{30} $ to calculate how much Samantha will have in her account in 2050.

I'll calculate this next.Samantha will have approximately **$9967.90** in her savings account by the year 2050.

Do you want more details or have any questions about the calculation?

Here are some related questions you might find interesting:
1. How would the result change if the interest were compounded monthly instead of annually?
2. What if Samantha had deposited an additional amount each year? How would that affect the total in 2050?
3. How can you calculate the time it takes for the account balance to double?
4. What is the difference between simple interest and compound interest in this context?
5. How would inflation impact the real value of Samantha's savings in 2050?

**Tip:** The longer money remains in a compound interest account, the more significant the growth due to the exponential nature of compounding.

In 2020, Samantha deposited $2,000 into a savings account that earns 5.5% interest annually. She doesn't deposit or withdraw any money from the account. Write an equation in the form A(t) = P(1 + r/100)^t that would predict the amount in the account for any year past 2020. (a) Write the equation. (b) If Samantha plans to retire in 2050, how much money will be in the account? Round your answer to the nearest cent.

Learn how to calculate compound interest with a $2000 deposit and 5.5% annual interest. Understand the formula A(t) = P(1 + r/100)^t and find out how much will be in the account after 30 years by solving this problem. Perfect for students in Grades 9-12.

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