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The problem in the image asks how much Emilia and Liam need to deposit monthly in order to save $160,000 over 10 years, with the money invested in an account paying 4% interest, compounded monthly.

This can be solved using the formula for the future value of a series of regular deposits into an account with compound interest:

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

Where:
- $A$ is the future value (amount they want to save, $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 (12 for monthly compounding),
- $t$ is the number of years (10 years).

We can rearrange the formula to solve for $P$:

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

Now, let's calculate the monthly deposit.Emilia and Liam need to deposit approximately **$1,086.59** per month in order to save $160,000 in 10 years, with a 4% interest rate compounded monthly.

Would you like more details on the calculation or further clarification?

Here are 5 related questions for further exploration:
1. How would the monthly deposit change if the interest rate were higher, say 5%?
2. What if the deposit frequency changed to weekly instead of monthly?
3. How would their savings differ if they started with an initial lump sum?
4. What is the total interest earned over the 10-year period?
5. What happens if the compounding is done annually instead of monthly?

**Tip**: Increasing the interest rate can significantly reduce the required monthly deposit to reach the same savings goal!

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 deposits needed to save $160,000 over 10 years with a 4% interest rate, compounded monthly. Understand the application of the compound interest formula and future value of annuities for practical financial planning. Ideal for students in Grades 10-12.

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