Explanation
This is a two step problem:
First, calculate the bond price using the yield information, then
Second, once you know the bond price, calculate the 18 month zero rate using the bootstrap method.
Step 1: Bond valuation: All variables required for pricing the bond are known. The coupon payments will be
$1.50 in 6 months and 1 year from now, and a final paymento of $101.50 will be received in an year's time.
This can be discounted at the yield provided as follows, and summed together to get the bond price of $97.14.
Step 2: Boot strapping: Discount the 6 month and 12 month coupons at the zero rates for those periods, and subtract the total of these PVs from the bond price. These work out to 1.5/(1+2%/2) = 1.485, and
1.5/(1+3%/2)^2=1.456. That gives us the present value, $97.14 - $1.485 - 1.456 = $94.203, which grows to the final payment of $101.50 at the end of 18 months. The zero rate inherent in this price can then be worked out as we know that (1+r/2)^3 = 101.5/94.203, or r = 5.03%.