Final answer:
The least amount you could pay for the Treasury bond, based on the ask price, is $1,026.15. Changes in interest rates affect bond prices; if rates go up, the price of this bond would decrease, potentially below its face value. In a 12% interest rate market, investors would not pay more than $964 for a bond with lower returns.
Step-by-step explanation:
To calculate the least amount you could pay to acquire a Treasury bond, you look at the ask price, as that is the price at which the seller is willing to sell the bond. The ask price is given as 102.615, which means the bond is priced at 102.615% of its $1,000 face value.
The least amount you would pay for the bond would be the ask price multiplied by the face value:
Price of bond
= (102.615 / 100) * $1,000
This gives us:
Price of bond
= 1.02615 * $1,000
= $1,026.15
So, the least you could pay for this bond is $1,026.15. However, considering changes in interest rates, specifically if the rates rise, the price of bonds will typically decrease, and vice versa. Hence, if the market interest rate is above the bond's coupon rate, you would generally expect to pay less than the bond's face value.
In an environment where the prevailing market interest rates rise to 12%, and a bond with a nearby maturity is only offering a return of 8%, the bond would sell for less than its face value to compensate for the lower interest return compared to the market rate. The price adjustment ensures that the yield on the bond matches or gets closer to what is available in the market. To induce an investor to buy an 8% bond in a 12% market, the bond's price must be decreased, potentially below the face value of $1,000.
Comparing an alternative investment that guarantees a 12% return, we can invest $964 to receive $1,080 in a year. Consequently, no rational investor would pay more than $964 for the bond because they could achieve a greater return by investing elsewhere.