Question 1193566
**1. Understand the Concept**

* **Present Value:** The current worth of a future sum of money, given a specific interest rate and time period. 
* **Compounding:** Interest is earned not only on the principal but also on the accumulated interest from previous periods.

**2. Identify the Given Values**

* **Future Value (FV):** $5200
* **Interest Rate (Annual):** 6.5% or 0.065
* **Time Period (Months):** 40 months
* **Compounding Frequency:** Quarterly (4 times per year)

**3. Calculate the Number of Periods**

* Since the interest is compounded quarterly, we need to find the total number of quarters:
   * Number of Quarters = (Number of Months) / 3 
   * Number of Quarters = 40 months / 3 months/quarter = 13.33 quarters 
   * **Round up to 14 quarters** (as we can't have a fraction of a quarter)

**4. Calculate the Quarterly Interest Rate**

* Quarterly Interest Rate = (Annual Interest Rate) / 4
* Quarterly Interest Rate = 0.065 / 4 = 0.01625

**5. Calculate the Present Value (PV)**

* Use the formula for present value with compound interest:
   PV = FV / (1 + r)^n 
   where:
      * PV = Present Value
      * FV = Future Value ($5200)
      * r = Quarterly Interest Rate (0.01625)
      * n = Number of Quarters (14)

* PV = $5200 / (1 + 0.01625)^14 
* PV = $5200 / (1.01625)^14 
* PV = $5200 / 1.2518 
* PV ≈ $4153.69

**Therefore, the discounted value now of $5200 due in 40 months, with an interest rate of 6.5% compounded quarterly, is approximately $4153.69.**