Question 1193566: Determine the discounted value now of $5200 due in 40 months if money is worth 6.5% compounded quarterly.
Answer by yurtman(42)   (Show Source):
You can put this solution on YOUR website! **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.**
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