Camden invested dollar sign, $1400 in an account that pays 4.5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Camden would have in the account 12 years after his initial investment. Round your answer to the nearest whole number

To calculate the amount of money Camden would have in the account after 12 years, 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 $ n $ years, including interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

In this problem:
- $ P = 1400 $ dollars
- $ r = 4.5\% = 0.045 $
- $ n = 1 $ (since the interest is compounded annually)
- $ t = 12 $ years

Substituting these values into the formula:

\[
A = 1400 \left(1 + \frac{0.045}{1}\right)^{1 \times 12}
\]

\[
A = 1400 \left(1 + 0.045\right)^{12}
\]

\[
A = 1400 \times \left(1.045\right)^{12}
\]

Now, calculate the value of $\left(1.045\right)^{12}$:

\[
A \approx 1400 \times 1.688
\]

\[
A \approx 2363.2
\]

Rounding to the nearest whole number, Camden would have approximately **$2363** in the account after 12 years.

Would you like more details or have any questions about this? Here are five related questions that might interest you:

1. How would the amount change if the interest was compounded semi-annually?
2. What would happen if the interest rate increased to 5%?
3. How much interest would Camden have earned after 12 years?
4. What would be the final amount if Camden had invested for 20 years instead of 12 years?
5. How would the amount differ if Camden had invested $2000 instead of $1400?

**Tip:** Compound interest grows faster when interest is compounded more frequently.

Learn how to calculate compound interest with an initial investment of $1400 at an annual interest rate of 4.5%. Understand the formula and steps involved in determining the final amount after 12 years.

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