To determine the price you would pay for each bond, we first need to understand how the quoted bond prices translate to actual dollar amounts given the face value of [tex]$1000.
### Steps to Calculate the Bond Prices:
1. Convert the quoted price to a fraction.
- For Bond ABC: The quoted price is \( 104 \frac{3}{4} \).
- For Bond XYZ: The quoted price is \( 100 \frac{1}{2} \).
2. Convert the mixed numbers to improper fractions or decimals for ease in calculation.
- For Bond ABC:
- \( 104 \frac{3}{4} = 104 + \frac{3}{4} = 104.75 \)
- For Bond XYZ:
- \( 100 \frac{1}{2} = 100 + \frac{1}{2} = 100.5 \)
3. Calculate the price paid based on the face value ($[/tex]1000) and the quoted price percentage.
- For Bond ABC:
- The quoted price is [tex]\( 104.75 \% \)[/tex] of the face value.
- Actual price = [tex]\( \frac{104.75}{100} \times 1000 = 1047.5 \)[/tex]
- For Bond XYZ:
- The quoted price is [tex]\( 100.5 \% \)[/tex] of the face value.
- Actual price = [tex]\( \frac{100.5}{100} \times 1000 = 1005.00 \)[/tex]
### Conclusion:
- For Bond ABC listed at [tex]\( 104 \frac{3}{4} \)[/tex], you would pay [tex]$1047.50.
- For Bond XYZ listed at \( 100 \frac{1}{2} \), you would pay $[/tex]1005.00.
These prices are what you would pay today based on the quoted bond prices, with the face value of each bond being $1000.
