Question
A bond with no expiration date has a face value of R10.00 and pays a fixed 10 percent interest. If the market price of the bond rises to R14.00, the annual yield approximately equals :
Answers
GPT-4o mini
To calculate the annual yield of a bond with no expiration date (often referred to as a perpetuity), you can use the formula for yield:
\[
\text{Yield} = \frac{\text{Annual Interest Payment}}{\text{Market Price}}
\]
In this case:
- The face value of the bond is R10.00, and it pays a fixed interest rate of 10%. Therefore, the annual interest payment is:
\[
\text{Annual Interest Payment} = 10\% \times \text{Face Value} = 0.10 \times 10 = R1.00
\]
- The market price of the bond is R14.00.
Now substituting these values into the yield formula:
\[
\text{Yield} = \frac{R1.00}{R14.00} \approx 0.0714 \text{ (or 7.14\%)}
\]
Thus, the annual yield of the bond is approximately **7.14%**.
\[
\text{Yield} = \frac{\text{Annual Interest Payment}}{\text{Market Price}}
\]
In this case:
- The face value of the bond is R10.00, and it pays a fixed interest rate of 10%. Therefore, the annual interest payment is:
\[
\text{Annual Interest Payment} = 10\% \times \text{Face Value} = 0.10 \times 10 = R1.00
\]
- The market price of the bond is R14.00.
Now substituting these values into the yield formula:
\[
\text{Yield} = \frac{R1.00}{R14.00} \approx 0.0714 \text{ (or 7.14\%)}
\]
Thus, the annual yield of the bond is approximately **7.14%**.