You want to save money to buy a new computer. If you deposit $100 a month at an  annual interest rate of 6% compounded monthly, how much money will you have saved  after a year? 

To calculate how much money you will have saved after a year, we use the future value formula for compound interest with regular monthly deposits:

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

Where:
- $FV$ is the future value (the amount saved after a year),
- $P$ is the monthly deposit (\$100),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of months (12 months in a year).

### Given:
- Monthly deposit, $P = 100$,
- Annual interest rate = 6%, so the monthly interest rate, $r = \frac{6\%}{12} = 0.005$,
- Total number of months, $n = 12$.

Now, let's calculate the future value.

\[
FV = 100 \times \frac{(1 + 0.005)^{12} - 1}{0.005}
\]  

Let me compute that for you.After one year of depositing $100 per month at an annual interest rate of 6% compounded monthly, you will have saved approximately **$1,233.56**.

Would you like more details or have any questions? Here are five related questions to think about:

1. How much more would you save after two years with the same monthly deposit and interest rate?
2. How would the amount change if the interest were compounded quarterly instead of monthly?
3. What would happen if the annual interest rate increased to 8%?
4. How much would you need to deposit monthly to save $2,000 in one year at the same interest rate?
5. How does compound interest differ from simple interest in this context?

**Tip:** Starting to save earlier can greatly increase the total amount due to the compounding effect!

You want to save money to buy a new computer. If you deposit $100 a month at an annual interest rate of 6% compounded monthly, how much money will you have saved after a year?

Discover how much you can save with a monthly deposit of $100 at a 6% annual interest rate compounded monthly. Learn to use the compound interest formula to calculate your future savings in one year. Suitable for high school students and financial planning beginners.

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