Table 1: Coupon Bond Prices and Coupon Payments. (Notice that the Cash Flows in years 1 through Year 3 already reflect the coupon payments and the par value at maturity.)

Bond	Price	Year 1	Year 2	Year 3
1 2 3	99.50 101.25 100.25	105 6 7	0 106 7	0 0 107

• Let Pi be the price of bond i (e.g., if i=1, then Pi=P1 for bond 1). Let ci denote the dollar coupon associated with bond i, and y1 as a one-year spot rate of interest. Then, we can denote the price of the first bond as

Then, using known data, solve for y1.

Finally, we can solve for the one-year implied zero price, z1, as follows:

Note: z1 is also referred to as the discount factor or the present value of a $1 to be received at time t in the future. The two terms to the right of the z1 equation are equivalent ways of finding the answer. They should give the same answer.

Following the same procedure, we can solve iteratively for y2 and z2, etc .

Note that, after solving for yi in one step it becomes a known value in the next step. For example, when solving for y2 and z2, P1, P2 and y1 are known values that you can just plug in the formula for P2 to find y2 and then solve for z2.

• Required task: Use the above procedure, called Bootstrapping to complete Table 2 below for maturities 2 and 3 (see question marks, ?).

(Note: I provided the answers for maturity 1, for illustration. However, you should show your work, i.e., show the steps you followed to reach the answers, including your work to verify the answers already provided).

Table 2: Implied Zeroes and Spot Rates. (Answers for maturity 1 are already given to you for illustration. This will not count in your grade.)

Maturity (Years)	Implied Zero (zi)	Spot Rate (yi)
1	z1 = 0.9476	y1 = 5.53%
2	z2 = ?	y2 = ?
3	z3 = ?	Y3 = ?