Question 1191374
Here's how to calculate the monthly deposit and the total interest earned:

**a) Calculating the Monthly Deposit:**

We'll use the future value of an ordinary annuity formula, which is:

FV = P * [((1 + r)^n - 1) / r]

Where:

* FV = Future Value ($800,000)
* P = Periodic Payment (what we want to find)
* r = Interest rate per period (10% per year, so 10%/12 per month, or 0.1/12)
* n = Number of periods (30 years * 12 months/year = 360 months)

Let's rearrange the formula to solve for P:

P = FV * [r / ((1 + r)^n - 1)]

Now, plug in the values:

P = $800,000 * [(0.1/12) / ((1 + 0.1/12)^360 - 1)]
P = $800,000 * [0.008333 / (1.008333^360 - 1)]
P = $800,000 * [0.008333 / (19.788 - 1)]
P = $800,000 * [0.008333 / 18.788]
P ≈ $353.91

So, you would need to deposit approximately $353.91 each month.

**b) Calculating the Total Interest Earned:**

1. **Calculate the total amount deposited:**
   Total Deposited = Monthly Deposit * Number of Months
   Total Deposited = $353.91 * 360
   Total Deposited ≈ $127,407.60

2. **Calculate the total interest earned:**
   Total Interest Earned = Future Value - Total Deposited
   Total Interest Earned = $800,000 - $127,407.60
   Total Interest Earned ≈ $672,592.40

Therefore, you will earn approximately $672,592.40 in interest.