How much would you need to deposit in an account each month in order to have $10,000 in the account in 5 years? Assume the account earns 2% interest.

To find out how much you would need to deposit monthly to have $10,000 in 5 years, assuming the account earns 2% interest compounded monthly, we can use the **Future Value of an Annuity formula**:

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

Where:
- $FV$ is the future value (in this case, $10,000),
- $P$ is the monthly deposit (the value we are solving for),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (number of months over 5 years).

### Steps to solve:
1. The interest rate is 2% per year, so the monthly interest rate $r$ is:
   \[
   r = \frac{2\%}{12} = \frac{0.02}{12} \approx 0.0016667
   \]

2. The number of payments $n$ for 5 years is:
   \[
   n = 5 \times 12 = 60
   \]

Now, we can rearrange the formula to solve for $P$ (the monthly deposit):

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

Substituting the values:
\[
P = \frac{10000 \times 0.0016667}{(1 + 0.0016667)^{60} - 1}
\]

Let me calculate that for you.To have $10,000 in the account in 5 years with a 2% interest rate compounded monthly, you would need to deposit approximately **$158.61** each month.

Would you like further details on the calculations, or do you have any other questions?

Here are 5 related questions for further exploration:
1. What if the interest rate was 3% instead of 2%?
2. How would the monthly deposit change if you wanted to reach $15,000 in 5 years?
3. What is the effect of compounding daily rather than monthly?
4. How much total interest would you earn over the 5 years?
5. How does increasing the deposit period to 10 years affect the monthly payment?

**Tip:** Always verify the compounding frequency when calculating interest—compounding monthly, daily, or annually can significantly affect your final savings.

Learn how to calculate the monthly deposit needed to save $10,000 in 5 years with 2% interest compounded monthly. This problem covers key financial concepts such as annuities and compound interest, and is ideal for high school students in Grades 10-12.

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