Kiran deposits $680 every month into an account earning an annual interest rate of 8.4% compounded monthly. How much would he have in the account after 2 years, *to the nearest dollar*?

To calculate how much Kiran would have in his account after 2 years with monthly deposits and compound interest, we use the formula for the future value of an annuity compounded monthly:

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

where:
- $ A $ is the amount in the account after $ t $ years.
- $ P $ is the monthly deposit ($680).
- $ r $ is the annual interest rate (8.4% or 0.084).
- $ n $ is the number of times the interest is compounded per year (12 for monthly).
- $ t $ is the number of years (2).

Plugging in the values:

\[ A = 680 \left( \frac{(1 + 0.084/12)^{12 \times 2} - 1}{0.084/12} \right) \]

First, calculate the monthly interest rate:

\[ r/n = \frac{0.084}{12} = 0.007 \]

Then, calculate $ (1 + 0.007)^{24} $:

\[ (1 + 0.007)^{24} = 1.007^{24} \approx 1.18365 \]

Now, use this to find the future value of the annuity:

\[ A = 680 \left( \frac{1.18365 - 1}{0.007} \right) \]
\[ A = 680 \left( \frac{0.18365}{0.007} \right) \]
\[ A = 680 \times 26.2357 \]
\[ A \approx 17,841.28 \]

Therefore, Kiran would have approximately $17,841 in the account after 2 years.

Would you like more details or have any questions? Here are some questions you might find interesting:

1. How does the monthly compounding affect the final amount compared to annual compounding?
2. What if Kiran changes the amount he deposits each month?
3. How would the final amount change if the interest rate was different?
4. What is the future value if Kiran stops depositing after 1 year?
5. How does the future value formula change if interest is compounded daily instead of monthly?

**Tip:** For accurate calculations, always ensure to use the correct compounding period and convert annual rates to the appropriate periodic rate when dealing with compound interest problems.

Learn how to calculate the future value of an investment account with monthly deposits and compound interest. This problem involves applying the formula for the future value of an annuity compounded monthly, with detailed step-by-step calculations. Suitable for students in Grades 10-12 studying compound interest and financial mathematics.

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