Final answer:
The present value of a government bond valued at $15,000 due in ten years at a 3.3% discount rate is calculated using the formula PV = FV / (1 + r)^n. An example with a simple two-year bond demonstrates how present value adjusts with changes in the discount rate.
Step-by-step explanation:
The student has asked about the present value of a government bond with a par value of $15,000 due ten years from today, at an annual discount rate of 3.3%. To calculate the present value, we use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value (par value of the bond), r is the discount rate, and n is the number of years until maturity.
Using the formula, the present value would be calculated as follows: PV = $15,000 / (1 + 0.033)^10. This calculation would provide the current worth of the bond, given the discount rate of 3.3% over the ten-year period until the bond's maturity.
To illustrate with an example, let's consider a simple two-year bond. If the bond has a par value of $3,000, pays 8% annual interest, and the current discount rate is 8%, the bond's PV would equal $3,000, as the interest and discount rates cancel each other out. However, if the discount rate rises to 11%, the present value would be recalculated using the higher discount rate, which would result in a decrease in the bond's present value.