Final answer:
To find the price of a Treasury bill, one must understand the discount rate and apply it to the face value to determine the current price and interest paid. For a bond, the present value formula is used to calculate its worth based on future payments, taking into account the interest rate and duration until maturity. These calculations allow investors to assess the value of these financial instruments in present terms.
Step-by-step explanation:
To answer the student's question about the Treasury bill (T-bill) and bond pricing, we use present value calculations. The price of a Treasury bill can be calculated by understanding the discount rate and the face value of the T-bill. In this scenario, with a six-month $15,000 T-bill at a discount rate of 2.170%, we need to find both the price and the actual interest paid by the Treasury. To calculate the actual price, we need to apply the formula for the present value of a T-bill. For bonds, the principle remains the same, where we look at the stream of future payments and apply a present value formula to determine its current worth, taking into account the interest rate and time period.
As an illustration, consider a simple two-year bond with an 8% interest rate. The bond pays $240 in interest each year, and its face value is returned at the end of the second year. If the discount rate is 8%, the present value of the bond’s payments must be calculated. However, if interest rates rise to 11%, the bond's present value will be recalculated at this new discount rate.
Example calculations for the bond at different discount rates would resemble the following:
- Discount rate of 8%: Present value = ($240 / (1 + 0.08)) + ($240 / (1 + 0.08)^2) + ($3,000 / (1 + 0.08)^2)
- Discount rate of 11%: Present value = ($240 / (1 + 0.11)) + ($240 / (1 + 0.11)^2) + ($3,000 / (1 + 0.11)^2)
In both cases, we discount future cash flows back to their present values.