Five years from today, you plan to invest $3,700 for 7 additional years at 5.8 percent compounded annually. How much will you have in your account 12 years from today?

Multiple Choice

$5,490.37

$5,876.82

$7,278.30

$5,994.05

$5,189.38

To solve this problem, we use the **compound interest formula**:

\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]

Where:
- $A$ is the amount of money in the account after time $t$.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year (since it's compounded annually, $n = 1$).
- $t$ is the number of years the money is invested.

### Given dataTo solve this problem, we use the **compound interest formula**:

\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]

Where:
- $A$ is the amount of money in the account after time $t$.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year (since it's compounded annually, $n = 1$).
- $t$ is the number of years the money is invested.

### Given 
- Initial investment $P = 3700$
- Annual interest rate $r = 5.8\% = 0.058$
- Time after investment $t = 7$ years (since the investment starts after 5 years and runs for 7 years)
- $n = 1$ (compounded annually)

Now, let's calculate the future value of the investment 12 years from today (7 years after the investment starts). 

\[
A = 3700 \left( 1 + \frac{0.058}{1} \right)^{1 \times 7}
\]

Let me calculate that.The amount you will have in your account 12 years from today is approximately **$5,490.37**.

This matches the first option in your multiple choice list.

Would you like further details or have any questions? Here are five related questions for deeper exploration:

1. How does the compound interest formula change if the interest is compounded semi-annually or quarterly?
2. What would the total amount be if you invested for a longer period, like 10 or 15 years?
3. How does the interest rate affect the final amount in compound interest calculations?
4. What is the difference between compound and simple interest for the same scenario?
5. How can you calculate the number of years needed to reach a specific investment goal using compound interest?

**Tip:** The earlier you start investing, the more time your money has to grow due to compounding effects!

Five years from today, you plan to invest $3,700 for 7 additional years at 5.8 percent compounded annually. How much will you have in your account 12 years from today?

Learn how to calculate the future value of a $3,700 investment over 7 years at an annual interest rate of 5.8%, compounded annually. Explore the compound interest formula and see how much your account will hold 12 years from today. Suitable for high school finance and math students.

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