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The problem in the image asks how much Emilia and Liam need to deposit each month into an account that pays 4% interest, compounded monthly, to save $160,000 over 10 years for a house.

This is a future value of an annuity problem, which can be solved using the formula:

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

Where:
- $FV$ is the future value (the amount they want to save) = $160,000
- $P$ is the monthly deposit (what we need to find)
- $r$ is the annual interest rate = 4% or 0.04
- $n$ is the number of times interest is compounded per year (monthly compounding means $n = 12$)
- $t$ is the number of years = 10

We will solve for $P$.

Let me compute that.Emilia and Liam need to deposit approximately **$1,086.59** each month in order to save $160,000 over 10 years, with an interest rate of 4% compounded monthly.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What would the monthly deposit be if the interest rate was 5% instead of 4%?
2. How would the monthly deposit change if they only had 5 years to save for the house?
3. What if Emilia and Liam already had $20,000 saved — how would this affect their monthly deposit?
4. How much interest will they have earned by the end of the 10 years?
5. What would happen to the monthly deposit if the interest was compounded quarterly instead of monthly?

**Tip**: Always check the compounding frequency (monthly, quarterly, etc.) when solving interest-related problems, as it affects the total amount saved.

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 the monthly deposit needed to save $160,000 over 10 years with a 4% interest rate, compounded monthly. This problem covers the future value of annuity concepts and compound interest formula. Suitable for college-level math students.

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