Question 1193367
Certainly, let's break down the calculations for these debt scenarios.

**1. Marry's Debt**

**1.1.1. Present Value of the Debt Now**

* **Given:** 
    * Future Value (FV) = 500 
    * Interest Rate (r) = 15% per year = 0.15 
    * Time (t) = 8 months = 8/12 years = 2/3 years

* **Simple Interest:** 
    * Interest = Principal * Rate * Time 
    * Interest = 500 * 0.15 * (2/3) = 50 

* **Present Value (PV):** 
    * PV = FV - Interest 
    * PV = 500 - 50 
    * PV = 450

**Therefore, the single payment Marry needs to make now is 450.**

**1.1.2. Present Value of the Debt Six Months from Now**

* **Time Remaining:** 8 months - 6 months = 2 months = 2/12 years = 1/6 years

* **Future Value (FV) at 6 months from now:** 500 (remains the same)

* **Simple Interest:** 
    * Interest = 500 * 0.15 * (1/6) = 12.50

* **Present Value (PV) at 6 months from now:** 
    * PV = FV - Interest 
    * PV = 500 - 12.50 
    * PV = 487.50

**Therefore, the single payment Marry needs to make six months from now is 487.50.**

**1.1.3. Present Value of the Debt in One Year**

* **Time Remaining:** 8 months - 12 months = -4 months (This means the due date has already passed)

* **Since the due date has already passed, Marry would need to pay the full amount plus interest accrued for the past 4 months.**

* **Interest Accrued:** 500 * 0.15 * (4/12) = 25

* **Total Payment:** 500 + 25 = 525

**Therefore, if the payment is due in one year, Marry needs to pay 525.**

**2. Promissory Note**

**2.1.1. Maturity Value of the Note**

* **Given:** 
    * Principal (P) = 15000 
    * Discount Rate (r) = 16% per year = 0.16 
    * Time (t) = 6 months (April 1 to October 1) = 6/12 years = 0.5 years

* **Discount:** 
    * Discount = P * r * t 
    * Discount = 15000 * 0.16 * 0.5 
    * Discount = 1200

* **Maturity Value (MV):** 
    * MV = Principal - Discount 
    * MV = 15000 - 1200 
    * MV = 13800

**Therefore, the maturity value of the note is 13800.**

**2.1.2. Present Value on the Date of Sale (July 1, 2021)**

* **Time Remaining to Maturity:** 3 months (July 1 to October 1) = 3/12 years = 0.25 years

* **Discount from Sale Date:** 
    * Discount = Maturity Value * r * t 
    * Discount = 13800 * 0.16 * 0.25 
    * Discount = 552

* **Present Value on the Date of Sale:** 
    * Present Value = Maturity Value - Discount 
    * Present Value = 13800 - 552 
    * Present Value = 13248

**Therefore, the present value of the note on the date of sale (July 1, 2021) is 13248.**