To determine the market price of the security, we need to calculate the present value of its future cash flows, which consist of periodic coupon payments and the redemption value.

Given information:

• Coupon rate: 10% per year (R4895 security)
• Coupon payments: 5% of the face value every 6 months (since interest is payable semiannually)
• Redemption value: 99% of face value at maturity on 28 February 2030
• Yield rate: 12.18% compounded semiannually
• Time to maturity: 10 years from 28 February 2020 to 28 February 2030
• Coupon periods: 2 per year (since interest is compounded semiannually)

Let’s calculate the market price step by step.

Step 1: Define the variables

• Face value (denoted $F$): R100
• Coupon payment every 6 months $C = 5\% \times 100 = 5$ per half-year
• Number of periods: $n = 2 \times 10 = 20$ (10 years × 2 payments per year)
• Redemption value $R = 99\% \times 100 = 99$
• Semiannual yield $i = \frac{12.18\%}{2} = 6.09\% \text{ per period}$

Step 2: Calculate the present value of the coupon payments

The present value of the coupon payments is given by the formula for the present value of an annuity:

$PV_{\text{coupons}} = C \times \frac{1 - (1 + i)^{-n}}{i}$

Substituting the values:

$PV_{\text{coupons}} = 5 \times \frac{1 - (1 + 0.0609)^{-20}}{0.0609}$

Step 3: Calculate the present value of the redemption value

The present value of the redemption value is given by the formula:

$PV_{\text{redemption}} = \frac{R}{(1 + i)^n}$

Substituting the values:

$PV_{\text{redemption}} = \frac{99}{(1 + 0.0609)^{20}}$

Step 4: Calculate the market price

The market price is the sum of the present value of the coupons and the present value of the redemption value:

$P = PV_{\text{coupons}} + PV_{\text{redemption}}$

Let's compute this value.

Calculation

1. $(1 + 0.0609)^{-20} = 0.311756$
2. $1 - 0.311756 = 0.688244$
3. $\frac{0.688244}{0.0609} = 11.302$
4. $PV_{\text{coupons}} = 5 \times 11.302 = 56.51$

For the redemption value:

1. $(1 + 0.0609)^{20} = 3.207$
2. $\frac{99}{3.207} = 30.87$

Now, summing these:

$P = 56.51 + 30.87 = 87.38$

Thus, the market price of the security on 28 February 2020 is 87.38.

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Would you like more details on any of the steps?

Here are five related questions:

1. How would the market price change if the yield rate were 10%?
2. What happens to the market price if the bond is redeemed at 100% instead of 99%?
3. How does compounding frequency affect bond pricing?
4. What is the relationship between bond prices and interest rates?
5. How can the present value of the bond's cash flows be derived for quarterly payments?

Tip: The higher the yield rate relative to the coupon rate, the lower the bond price, and vice versa.