1600 dollars is placed in an account with an annual interest rate of 5.25%. How much will be in the account after 25 years, *to the nearest cent*?

To calculate the amount in the account after 25 years with an annual interest rate of 5.25%, we can use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial investment), which is $1600.
- $ r $ is the annual interest rate (decimal), which is 5.25% or 0.0525.
- $ n $ is the number of times the interest is compounded per year. If the problem doesn't specify, we assume it is compounded annually, so $ n = 1 $.
- $ t $ is the time the money is invested for, which is 25 years.

Now, we can plug in the values:

\[
A = 1600 \left(1 + \frac{0.0525}{1}\right)^{1 \times 25}
\]

\[
A = 1600 \left(1.0525\right)^{25}
\]

Let's calculate the result.The amount in the account after 25 years will be approximately **$5750.06** to the nearest cent.

Do you want more details or have any questions?

Here are 8 related questions for further exploration:
1. What would be the amount if the interest were compounded monthly instead of annually?
2. How much interest is earned over the 25 years?
3. What would the total amount be if the interest rate was 6% instead of 5.25%?
4. How long would it take for the investment to double at this interest rate?
5. What is the effective annual rate (EAR) for this investment?
6. How would the final amount change if an additional $100 were added each year?
7. What if the initial amount were $2000 instead of $1600?
8. How would the amount change if the investment period was 30 years instead of 25?

**Tip:** Understanding how compound interest works is crucial for long-term financial planning and can help you maximize your investments.

Learn how to calculate compound interest on an investment of $1600 at an annual rate of 5.25% over 25 years. Understand the formula and steps involved in computing the future value of investments using compound interest.

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