Question 1193578
### 1.1. Amount the Client Will Receive

The client signs a note to pay \( M = 6000 \) in nine months. The bank uses a simple discount rate formula:

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

Where:
- \( M = 6000 \) (maturity value),
- \( d = 0.16 \) (simple discount rate per annum),
- \( t = \frac{9}{12} = 0.75 \) years (time until maturity).

Substituting:

\[
PV = 6000 \times (1 - 0.16 \times 0.75)
\]

\[
PV = 6000 \times (1 - 0.12)
\]

\[
PV = 6000 \times 0.88
\]

\[
PV = 5280
\]

The client will receive **R5280**.

---

### 1.2. Equivalent Simple Interest of the Loan

To find the equivalent simple interest, we first determine the **interest amount** and then calculate the equivalent simple interest rate (\( r \)).

#### Interest Amount:
\[
\text{Interest} = M - PV = 6000 - 5280 = 720
\]

#### Equivalent Simple Interest Formula:
\[
\text{Interest} = PV \times r \times t
\]

Rearranging for \( r \):

\[
r = \frac{\text{Interest}}{PV \times t}
\]

Substitute the values:

\[
r = \frac{720}{5280 \times 0.75}
\]

\[
r = \frac{720}{3960}
\]

\[
r \approx 0.1818 \, \text{or } 18.18\%
\]

The equivalent simple interest rate is **18.18% per annum**.

---

### Final Summary:

1. **Amount Received by the Client**: \( R5280 \)
2. **Equivalent Simple Interest Rate**: \( 18.18\% \) per annum