To find the amount of money in the account after 6 years with monthly deposits of $299 at a 3% annual interest rate compounded monthly, we can use the future value of an annuity formula:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

where:

• $P$ is the monthly deposit amount,
• $r$ is the monthly interest rate,
• $n$ is the total number of deposits.

Given:

• $P = 299$ (monthly deposit),
• Annual interest rate = 3%, so the monthly interest rate $r = \frac{3\%}{12} = 0.0025$,
• Time $= 6$ years, so the number of deposits $n = 6 \times 12 = 72$.

Plugging in the values:

$FV = 299 \times \frac{(1 + 0.0025)^{72} - 1}{0.0025}$

Calculating this:

1. $(1 + 0.0025)^{72} = 1.1967$,
2. $1.1967 - 1 = 0.1967$,
3. $\frac{0.1967}{0.0025} = 78.68$,
4. $FV = 299 \times 78.68 = 23523.32$.

Rounding to the nearest dollar, the amount in the account will be approximately:

$\boxed{23,523}$

Would you like further details on this calculation, or do you have any questions?

Related Questions:

1. How does compounding frequency affect the future value of an investment?
2. What is the difference between future value and present value in annuities?
3. How would the amount change if the interest rate was compounded quarterly instead of monthly?
4. How does increasing the monthly deposit impact the future value after 6 years?
5. What would the future value be if the deposit period was extended to 10 years?

Tip: When calculating future values, always check the compounding period (monthly, quarterly, annually) as it significantly impacts the result.