Julieta and Eric are purchasing a home. They wish to save money for 10 years and purchase a house that has a value of $170,000 with cash. If they deposit money into an account paying 7% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase? Round your answer to the nearest cent, if necessary.

To determine how much Julieta and Eric need to deposit each month, we can use the **future value of an annuity formula** for monthly payments with compound interest. The formula is:

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

Where:
- $FV$ is the future value (the amount they want to have, which is $170,000),
- $P$ is the monthly payment (which we are solving for),
- $r$ is the annual interest rate (7%, or 0.07),
- $n$ is the number of compounding periods per year (since the interest is compounded monthly, $n = 12$),
- $t$ is the number of years (10 years).

We can now rearrange the formula to solve for $P$ (the monthly payment):

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

Now, plugging in the values:
- $FV = 170,000$,
- $r = 0.07$,
- $n = 12$,
- $t = 10$,

we can compute the monthly payment. I'll calculate it for you.Julieta and Eric will need to deposit approximately **$982.18** each month in order to save $170,000 in 10 years, assuming a 7% interest rate compounded monthly.

Do you have any questions, or would you like further details?

Here are 5 related questions to deepen understanding:
1. How does the interest rate affect the monthly payment?
2. What if the interest were compounded quarterly instead of monthly?
3. How much total interest would they earn over the 10 years?
4. What if Julieta and Eric could only afford $800 per month? How much would they save in 10 years?
5. How would the savings change if they saved for 15 years instead of 10?

**Tip:** Always ensure that the compounding frequency matches the interest compounding specified in the problem when using these formulas.

Discover how to calculate the monthly deposit needed to save $170,000 in 10 years with a 7% interest rate compounded monthly. Learn about compound interest and annuity formulas, perfect for students in Grades 11-12 and college-level math.

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