Final answer:
The market price of the Treasury bond quoted at 105:10 with a face value of $5,000 is $5,265.63. If interest rates have increased, the bond's market price would likely be below face value; if rates have decreased, above face value.
Step-by-step explanation:
When a Treasury bond is quoted at a price of 105:10, it means that the bond is trading at 105 and 10/32 percent of its face value.
To determine the market price of the bond, you convert the fractional price to a decimal and multiply it by the face value.
In this case:
105:10 is equivalent to 105.3125 percent (since 10/32 = 0.3125). Therefore, the market price is 1.053125 × $5,000 = $5,265.63.
Given the change in interest rates, if they have risen since the bond was issued, you could expect the market price of the bond to be less than its face value if you were to sell it before maturity.
This is because new bonds would likely be observed with higher interest rates, making the older bonds with lower coupon rates less attractive.
Conversely, if the rates fell, the bond price would typically be more than the face value.