Final answer:
The price of a one-year T-bill is calculated using the given forward rate and the basic present value formula. The spot rate Z2 can be found by comparing the theoretical price to the given market price and applying the provided formula. The valuation of bonds varies with changes in the discount rate, which affects their present value.
Step-by-step explanation:
The question involves using forward rates to calculate the price of a Treasury bill (T-bill) and compare it against a given market price to find the unknown spot rate, referred to as Z2. Let's tackle each part of the question step by step.
a. To calculate the price of a T-bill with one year to maturity using the given forward rate f0=0.03 (3%), and considering that T-Bills pay no coupons, the price P can be calculated as:
P = Par Value / (1 + f0)
= $100 / (1 + 0.03)
= $100 / 1.03
= $97.087
b. Given the actual price of the T-Bill is $93.804, we need to find Z2, which represents the spot rate for two periods (semi-annual). We would use the bond pricing formula considering the semi-annual periods.
c. To find the theoretical value of Z2, we use the equation (1+Znn) = (1+f0)(1+f1)... (1+fn-1). The student should substitute the given forward rates into this equation to solve for the correct spot rate, ensuring that the periods align (i.e., if considering semi-annual periods, then the compounding should also be semi-annual).
Following the formula provided and the information on bond valuation, an investor will be able to calculate the present value of the bond both with the original discount rate and with an increased discount rate, accounting for interest payments and the face value returned at maturity.