You deposit $300 each month into an account earning 8% interest compounded monthly. How much will be in the account in 15 years? 

This is a problem involving compound interest with regular monthly deposits. The formula to calculate the future value $ A $ of an annuity (regular deposits) compounded monthly is:

\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ A $ = Future value of the investment/loan, including interest
- $ P $ = Monthly deposit ($300 in this case)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments (number of months)

Let's break down the values:
- $ P = 300 $ (monthly deposit)
- Annual interest rate = 8%, so monthly interest rate $ r = \frac{8\%}{12} = 0.00667 $
- Number of months in 15 years = $ 15 \times 12 = 180 $

Now, we can substitute these values into the formula to find the future value.

\[
A = 300 \times \frac{(1 + 0.00667)^{180} - 1}{0.00667}
\]

Let's calculate this value.The amount in the account after 15 years, with monthly deposits of $300 and an 8% interest rate compounded monthly, will be approximately **$103,811.47**.

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

Here are 5 related questions to expand on this concept:
1. What would happen if the interest rate were 6% instead of 8%?
2. How does the length of time affect the total amount accumulated in the account?
3. What if you made a single lump-sum deposit instead of monthly contributions?
4. How would the future value change if the interest were compounded quarterly instead of monthly?
5. What if you increased the monthly deposit amount to $500?

**Tip**: The longer you leave money in a compound interest account, the more significant the interest becomes due to the compounding effect!

You deposit $300 each month into an account earning 8% interest compounded monthly. How much will be in the account in 15 years?

Learn how to calculate the future value of monthly $300 deposits at 8% interest compounded monthly for 15 years. This detailed guide uses the future value of annuity formula and explains the time value of money concept. Perfect for high school students studying finance or algebra.

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