To calculate the 2-year zero-coupon rate using bootstrapping:

1. For the 1-year bond: The 1-year spot rate equals the 1-year par rate = 4.15%

2. For the 2-year bond with 5.25% coupon:

   • Price = 100 = 5.25/(1 + z₁) + 105.25/(1 + z₂)²
   • Where z₁ = 4.15% (1-year spot rate)
   • 100 = 5.25/(1.0415) + 105.25/(1 + z₂)²
   • 100 = 5.04 + 105.25/(1 + z₂)²
   • 94.96 = 105.25/(1 + z₂)²
   • (1 + z₂)² = 105.25/94.96 = 1.1083
   • 1 + z₂ = √1.1083 = 1.0528
   • z₂ = 5.28%

The 2-year zero-coupon rate is approximately 5.28%.