Question 1209539
Here's how to solve this problem:

**1. Calculate the present value of the withdrawals:**

We need to find the present value of the series of withdrawals at the *start* of the withdrawal period.  This is because the withdrawals are made over time, and we need to discount them back to a single point in time to determine how much money is needed at the start of the withdrawals.

We can treat the withdrawals as an ordinary annuity.  The formula for the present value of an ordinary annuity is:

PV = PMT * [1 - (1 + r)^-n] / r

Where:

* PV = Present Value
* PMT = Periodic Payment (withdrawal amount) = $35,600
* r = Interest rate per period = 3.4% = 0.034
* n = Number of periods (withdrawals) = 5

PV = $35,600 * [1 - (1 + 0.034)^-5] / 0.034
PV = $35,600 * [1 - 0.8562] / 0.034
PV ≈ $35,600 * 4.2221
PV ≈ $150,200.32

**2. Discount the present value back to the start of the contributions:**

Gabriella and Mario make their last contribution 5 years *before* the withdrawals begin.  We need to discount the present value of the withdrawals back another 5 years to the end of the contributions.

PV_start = PV / (1 + r)^t

Where:

* PV_start = The present value at the start of the contributions
* PV = Present value of withdrawals = $150,200.32
* r = Interest rate = 0.034
* t = Number of years = 5

PV_start = $150,200.32 / (1 + 0.034)^5
PV_start ≈ $150,200.32 / 1.1803
PV_start ≈ $127,248.04

**3. Calculate the yearly contribution:**

Now we know how much money they need to have saved at the *end* of their 9 years of contributions. Their contributions are also an ordinary annuity so we use the future value of an ordinary annuity formula to find the yearly contribution.

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

Where:

* FV = Future Value = $127,248.04
* PMT = Periodic Payment (yearly contribution) - what we are solving for
* r = Interest rate = 0.034
* n = Number of periods (contributions) = 9

Rearranging the formula to solve for PMT:

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

PMT = $127,248.04 * 0.034 / [(1 + 0.034)^9 - 1]
PMT ≈ $4,326.43 / [1.3669 -1]
PMT ≈ $4,326.43/0.3669
PMT ≈ $11,791.80

**Answer:**

Gabriella and Mario must make yearly contributions of approximately $11,791.80.