Dominic invested $19,000 in an account paying an interest rate of 6.1% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 16 years?

To calculate the future value of Dominic's investment, we can use the formula for compound interest:

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

Where:
- $A$ is the amount of money in the account after $t$ years,
- $P$ is the initial principal (amount invested),
- $r$ is the annual interest rate (in decimal form),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the number of years.

Given:
- $P = 19,000$,
- $r = 6.1\% = 0.061$,
- $n = 12$ (since the interest is compounded monthly),
- $t = 16$ years.

Let's substitute these values into the formula and calculate $A$.

\[
A = 19000 \left(1 + \frac{0.061}{12}\right)^{12 \times 16}
\]After 16 years, Dominic's investment would grow to approximately **$50,298**.

Would you like more details or have any other questions?

Here are some related questions you might find helpful:
1. What if the interest rate was different, like 5% instead of 6.1%?
2. How does the frequency of compounding affect the total amount earned?
3. What would happen if Dominic made additional monthly deposits?
4. How would the calculation change if the interest were compounded quarterly?
5. What is the difference between simple and compound interest over long periods?

**Tip:** Increasing the frequency of compounding (e.g., from yearly to monthly) results in a slightly higher final amount, even if the interest rate remains the same.

Learn how to calculate the compound interest on an investment of $19,000 at an annual rate of 6.1%, compounded monthly over 16 years. This problem covers key financial math concepts, such as exponential growth and the compound interest formula. Suitable for high school students in Grades 10-12.

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