Deposits of $300 are made at the end of each month into an account that pays 9% annual interest compounded monthly. At the end of 25 years the account will have a value of


To determine the future value of an account with regular deposits, we can use the **future value of an annuity formula** for compound interest:

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

Where:
- $FV$ is the future value of the account.
- $P$ is the monthly deposit amount.
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of deposits (number of years multiplied by 12).

Given:
- $P = 300$ (monthly deposit),
- Annual interest rate $= 9\%$, so monthly interest rate $r = \frac{9\%}{12} = 0.0075$,
- The total number of months over 25 years $n = 25 \times 12 = 300$.

Now, let's calculate the future value.

\[
FV = 300 \times \frac{(1 + 0.0075)^{300} - 1}{0.0075}
\]

Let me calculate this for you.The future value of the account after 25 years of making monthly deposits of $300, at 9% annual interest compounded monthly, will be approximately **$336,336.58**.

Would you like further details on how this was calculated or do you have any additional questions?

Here are some related questions to deepen your understanding:
1. How would the future value change if the interest rate were 8% instead of 9%?
2. What if deposits were made at the beginning of each month instead of the end?
3. How does the future value change if the deposit amount is increased to $500 per month?
4. What if the compounding frequency was quarterly instead of monthly?
5. How can the present value of such an annuity be calculated?

**Tip**: Increasing the deposit frequency or amount can significantly grow the future value due to the effect of compounding interest.

Deposits of $300 are made at the end of each month into an account that pays 9% annual interest compounded monthly. At the end of 25 years the account will have a value of

Calculate the future value of monthly deposits of $300 at an annual interest rate of 9% compounded monthly over 25 years. This problem demonstrates the use of the future value of annuity formula, exponential growth, and the impact of compounding interest. Suitable for high school students in Grades 10-12.

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