Question 1193367: Kindly requesting your help about homework.
1. Marry owes 500 due in eight months, for each of the following cases, what single payment will his debt if simple interest rate is 15%p.a.
1.1.1. Now
1.1.2. Six months from now.
1.1.3. in one year.
2. A promissory note dated 1 April 2021 for 15000, borrowed at a simple discount rate of 16%p.a. due on the 1 October 2021 is sold on the 1 July 2021
2.1.1. what is the maturity value of the note?
2.1.2. What is the present value on the date of sale?
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! 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.**
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