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The question from the image asks:

"Emilia and Liam are purchasing a home. They wish to save money for 10 years and purchase a house that has a value of $160,000 with cash. If they deposit money into an account paying 4% 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 solve this, we can use the formula for the future value of a series of monthly deposits into an account with compound interest:

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

Where:
- $ FV $ is the future value ($160,000),
- $ P $ is the monthly deposit,
- $ r $ is the annual interest rate (4% or 0.04),
- $ n $ is the number of times interest is compounded per year (monthly, so 12),
- $ t $ is the time in years (10 years).

Rearranging the formula to solve for $ P $:

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

Let's plug in the values and compute.The monthly deposit Emilia and Liam need to make in order to save $160,000 in 10 years, with 4% interest compounded monthly, is approximately **$1,086.59**.

Would you like further explanation or details on any step of this calculation?

Here are five related questions to expand your understanding:
1. What happens if the interest rate changes to 5%?
2. How would the calculation change if the compounding frequency was quarterly instead of monthly?
3. What would be the total interest earned over the 10-year period?
4. How does compound interest differ from simple interest in this scenario?
5. What if Emilia and Liam already have some initial savings; how would the deposit amount change?

**Tip:** Compounding frequency significantly affects savings growth. Monthly compounding yields more interest than quarterly compounding at the same rate.

Emilia and Liam are purchasing a home. They wish to save money for 10 years and purchase a house that has a value of $160,000 with cash. If they deposit money into an account paying 4% 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.

Learn how to calculate monthly deposits needed to save $160,000 in 10 years with a 4% interest compounded monthly. Includes the formula for future value of savings and the breakdown of the solution step-by-step. Perfect for college-level financial mathematics or algebra students.

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