Question 1172965
Here's how to calculate the cost of the washing machine:

**Understanding the Problem**

* **Monthly Payments:** The household will pay $3000 per month for 6 months.
* **Interest:** The interest rate is 9% per year, compounded semi-annually.
* **Goal:** We need to find the present value of these payments, which represents the initial cost of the washing machine.

**Calculations**

Here's how we'll break down the calculation:

1.  **Semi-annual Interest Rate:**
    * The annual interest rate is 9% (0.09).
    * Since it's compounded semi-annually, the interest rate per period is 0.09 / 2 = 0.045.

2.  **Adjusting for Monthly Payments:**
    * Since the payments are monthly and the interest is compounded semi annually, this calculation becomes complex. The provided code assumes that the semi annual interest rate can be devided by the number of compounding periods, however this is incorrect.
    * To get a more accurate result, it is better to calculate the effective monthly rate.
    * The effective annual rate is (1 + 0.045)^2 = 1.092025. Meaning the effective annual rate is 9.2025%.
    * To get the monthly rate we calculate (1.092025)^(1/12) - 1 = 0.00739268. Meaning the monthly rate is 0.739268%.

3.  **Present Value of an Ordinary Annuity:**
    * We'll use the present value of an ordinary annuity formula:
        * PV = PMT * \[1 - (1 + r)^-n] / r
        * Where:
            * PV = Present Value (the cost of the washing machine)
            * PMT = Monthly Payment ($3000)
            * r = monthly interest rate (0.00739268)
            * n = Number of Payments (6)

4.  **Applying the Formula:**
    * PV = 3000 * \[1 - (1 + 0.00739268)^-6] / 0.00739268
    * PV = 3000 * \[1 - (1.00739268)^-6] / 0.00739268
    * PV = 3000 * \[1 - 0.956795] / 0.00739268
    * PV = 3000 * \[0.043205] / 0.00739268
    * PV = 3000 * 5.84422
    * PV = 17532.66

**Answer**

The cost of the washing machine is approximately $17532.66.