Question 1193456
**1. Calculate the Future Value of the Obligation:**

* **Given:**
    * Principal: $80,000
    * Interest Rate: 10% per year compounded quarterly (0.10/4 = 0.025 per quarter)
    * Number of Periods: 4 years * 4 quarters/year = 16 quarters

* **Formula:**
    * Future Value (FV) = Principal * (1 + Interest Rate per Period)^(Number of Periods)
    * FV = $80,000 * (1 + 0.025)^16
    * FV = $80,000 * 1.50945 
    * FV = $120,756

**2. Calculate the Present Value of the Obligation:**

* **a. Now:**
    * **Discount Rate:** 14% per year compounded quarterly (0.14/4 = 0.035 per quarter)
    * **Number of Periods:** 4 years * 4 quarters/year = 16 quarters

    * **Formula:**
        * Present Value (PV) = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
        * PV = $120,756 / (1 + 0.035)^16
        * PV = $120,756 / 1.7947
        * PV = $67,278.31

* **b. At the end of 3 years:**
    * **Future Value at the end of 3 years:** $120,756 (calculated above)
    * **Discount Period:** 1 year * 4 quarters/year = 4 quarters

    * **Formula:**
        * PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
        * PV = $120,756 / (1 + 0.035)^4
        * PV = $120,756 / 1.1475
        * PV = $105,220.41

* **c. At the end of 6.5 years:**
    * **Future Value at the end of 6.5 years:** $120,756 (calculated above)
    * **Discount Period:** (6.5 - 4) years * 4 quarters/year = 10 quarters

    * **Formula:**
        * PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
        * PV = $120,756 / (1 + 0.035)^10
        * PV = $120,756 / 1.4106
        * PV = $85,613.59

**Therefore:**

* **a. Value of obligation now:** $67,278.31
* **b. Value of obligation at the end of 3 years:** $105,220.41
* **c. Value of obligation at the end of 6.5 years:** $85,613.59