Question 1208431
Here's how to calculate the weekly savings amount and total interest earned:

**1. Calculate the quarterly interest rate:**

* Annual interest rate: 4.25% = 0.0425
* Quarterly interest rate: 0.0425 / 4 = 0.010625

**2. Calculate the total number of compounding periods:**

* Number of years: 7
* Compounding periods per year: 4
* Total compounding periods: 7 * 4 = 28

**3. Use the future value of an ordinary annuity formula:**

The future value (FV) of an ordinary annuity is the total value of a series of equal payments (in this case, weekly savings) at the end of each period, with interest accumulating over time. The formula is:

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

Where:

* FV = Future Value ($65,000 down payment)
* P = Periodic payment (weekly savings - what we need to find)
* r = Interest rate per period (quarterly rate)
* n = Number of periods (number of quarters)

Since we are saving weekly and interest is compounded quarterly, we need to adjust the formula a bit. We'll consider the total amount saved over the 7 years as the total amount of the annuity, and solve for the weekly payment.

**4. Adjust and solve for the weekly payment (P):**

Since contributions are weekly and compounding is quarterly, we can approximate the future value formula to solve for weekly contributions.
FV ≈ P * weeks per year * years * (((1 + r)^n - 1) / r)

$65,000 ≈ P * 52 * 7 * (((1 + 0.010625)^28 - 1) / 0.010625)

$65,000 ≈ P * 364 * (32.539)

$65,000 ≈ P * 11,843.27

P ≈ $65,000 / 11,843.27

P ≈ $5.49 per week

**5. Calculate the total amount saved:**

* Weekly savings: $5.49
* Weeks per year: 52
* Number of years: 7
* Total saved: $5.49 * 52 * 7 = $2002.36

**6. Calculate the total interest earned:**

* Down payment goal: $65,000
* Total saved: $2002.36
* Total interest earned: $65,000 - $2002.36 = $62,997.64

**Answer:**

* **[Blank-1]:** Their weekly savings amount would have to be approximately $5.49.
* **[Blank-2]:** The total interest earned would be approximately $62,997.64.