We need to use bootstrapping to find the spot rates. We first find the 6-month implied spot rate from the first bond and then use this to find the 12-month implied spot rate from the second bond.

Step 1: Find the implied 6-month spot rate.

6-month bond price = cash flows / (1 + r₁ / 2)
$102.2969 = (100 + 3.10) / (1 + r₁ / 2)$r₁ = 2 × [(`$103.10/$102.29`69) - 1] = 1.57%

Step 2: Use the implied 6-month spot rate to find the implied 12-month spot rate.

$104.0469 = 3.2 / (1 + 0.0157 / 2) + 103.2 / (1 + r₂ / 2)²$`$100.8718 = 103.2 / (1 + r₂ / 2)²$ r₂ = 2 × [($103.2` / `$100.87`18)¹/² - 1] = 2.29%

(Book 3, Module 42.2, LO 42.j)