Question 1193568
### 1. Ben's Debt Repayment with Simple Interest at 15% p.a.

The formula for simple interest is:

\[
A = P \times (1 + r \times t)
\]

Where:
- \( A \): Repayment amount,
- \( P = 500 \): Principal,
- \( r = 0.15 \): Annual simple interest rate,
- \( t \): Time in years.

---

#### 1.1. Single Payment **Now**

If Ben repays the debt **now**, no interest has accrued yet:

\[
A = P = 500
\]

---

#### 1.2. Single Payment **Six Months from Now**

From now to six months (\( t = \frac{6}{12} = 0.5 \) years), interest accrues:

\[
A = 500 \times (1 + 0.15 \times 0.5)
\]

\[
A = 500 \times (1 + 0.075)
\]

\[
A = 500 \times 1.075 = 537.50
\]

---

#### 1.3. Single Payment **In One Year**

From now to one year (\( t = \frac{12}{12} = 1 \) year), interest accrues:

\[
A = 500 \times (1 + 0.15 \times 1)
\]

\[
A = 500 \times (1 + 0.15)
\]

\[
A = 500 \times 1.15 = 575
\]

---

### 2. Promissory Note at a Simple Discount Rate of 16% p.a.

#### 2.1. Maturity Value of the Note

The **maturity value** of the note is the amount due at the end of the loan period. For this case, it is explicitly given as **R1500**.

---

#### 2.2. Present Value on the Date of Sale

The note has a simple discount rate of 16% p.a., and the present value is calculated using:

\[
PV = M \times (1 - d \times t)
\]

Where:
- \( M = 1500 \) (maturity value),
- \( d = 0.16 \) (discount rate),
- \( t \): Time remaining to maturity in years. From 1 July 2021 to 1 October 2021 is 3 months or \( t = \frac{3}{12} = 0.25 \) years.

Substitute the values:

\[
PV = 1500 \times (1 - 0.16 \times 0.25)
\]

\[
PV = 1500 \times (1 - 0.04)
\]

\[
PV = 1500 \times 0.96
\]

\[
PV = 1440
\]

---

### Final Summary

#### 1. Ben's Debt Repayment:
1. **Now**: \( R500 \),
2. **Six Months from Now**: \( R537.50 \),
3. **In One Year**: \( R575 \).

#### 2. Promissory Note:
1. **Maturity Value**: \( R1500 \),
2. **Present Value on Sale Date (1 July 2021)**: \( R1440 \).