Determine the market price on 28 February 2020 of a 10%, R4894 security, with interest payable on 28 February and 31 August. The security is redeemable on 28 February 2029 at R108% and the investor wants to earn a yield rate of 11.44% per year, compounded twice per year. 

To determine the market price of the security, we use the present value formula for bonds, which takes into account the periodic coupon payments, the redemption amount, and the desired yield rate. Here's the step-by-step process:

### Step 1: Gather Information
- **Coupon Rate (C):** 10% of the face value.
- **Interest Payment Dates:** 28 February and 31 August each year.
- **Redemption Date:** 28 February 2029.
- **Redemption Price (F):** 108% of face value (assuming face value = 100, redemption price = 108).
- **Yield Rate (r):** 11.44% per year compounded semi-annually. Thus, each half-year period has a yield rate of \( r = \frac{11.44\%}{2} = 5.72\% \) per period.
- **Number of Periods (n):** Since the bond matures on 28 February 2029, the number of half-year periods from 28 February 2020 is:
  \[
  n = 2 \times (2029 - 2020) = 18 \text{ half-year periods}.
  \]

### Step 2: Coupon Payment Calculation
The coupon payment is 10% of the face value, paid semi-annually. Assuming a face value of 100, the coupon payment (denoted as \( C \)) is:
\[
C = \frac{10\% \times 100}{2} = 5 \text{ units per period}.
\]

### Step 3: Present Value of Coupon Payments
The present value of the coupon payments is calculated using the present value of an annuity formula:
\[
PV_{\text{coupons}} = C \times \left( 1 - (1 + r)^{-n} \right) / r
\]
Substituting the values:
\[
PV_{\text{coupons}} = 5 \times \left( 1 - (1 + 0.0572)^{-18} \right) / 0.0572
\]
Calculating this step-by-step:

\[
1 + 0.0572 = 1.0572
\]
\[
(1.0572)^{-18} \approx 0.39574
\]
\[
1 - 0.39574 = 0.60426
\]
\[
PV_{\text{coupons}} = 5 \times \frac{0.60426}{0.0572} \approx 5 \times 10.5635 = 52.8175
\]

### Step 4: Present Value of Redemption Payment
The redemption payment of 108 units is paid at the end of 18 periods. The present value of this lump sum is:
\[
PV_{\text{redemption}} = F \times (1 + r)^{-n}
\]
Substituting the values:
\[
PV_{\text{redemption}} = 108 \times (1.0572)^{-18}
\]
We already calculated \( (1.0572)^{-18} \approx 0.39574 \), so:
\[
PV_{\text{redemption}} = 108 \times 0.39574 = 42.744
\]

### Step 5: Total Present Value (Market Price)
The total present value, which represents the market price of the bond, is the sum of the present values of the coupon payments and the redemption payment:
\[
\text{Market Price} = PV_{\text{coupons}} + PV_{\text{redemption}} = 52.8175 + 42.744 = 95.5615
\]

Thus, the **market price** of the bond on 28 February 2020 is approximately **95.56 units**.

---

Would you like more details or explanations on any part? 

Here are 5 related questions for further exploration:
1. How does changing the yield rate affect the bond price?
2. What would the market price be if the yield rate was 10%?
3. How would the market price change if the bond was redeemable at 100% instead of 108%?
4. What is the difference between current yield and yield to maturity?
5. How are bonds priced when interest is paid annually instead of semi-annually?

**Tip:** When bond prices decrease as interest rates rise, it's known as "interest rate risk."

Determine the market price on 28 February 2020 of a 10%, R4894 security, with interest payable on 28 February and 31 August. The security is redeemable on 28 February 2029 at R108% and the investor wants to earn a yield rate of 11.44% per year, compounded twice per year.

Learn how to calculate the market price of a 10% R4894 security with semi-annual coupon payments and a redemption rate of 108%, using an 11.44% yield compounded semi-annually. This step-by-step solution includes key financial concepts like present value of coupons and redemption payments. Suitable for finance students and professionals.

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