The bond with 6 months left to maturity has a semiannual discount rate of 0.01/2 = 0.005 therefore the 1-year spot rate can be found by solving the following equation:

0.75/1.005 + 100.75/(1 + S_1.0/2)² = 100

Solving for S_1.0/2: 100.75/(1 + S_1.0/2)² = 100 - 0.75/1.005

100.75/(1 + S_1.0/2)² = 99.2537

100.75 / 99.2537^0.5 = (1 + S_1.0/2)²

(100.75 / 99.254)^.5 – 1 = S_1.0/2

0.007509 = S_1.0/2

2 × 0.007509= S_1.0

S_1.0 = 0.01502 or 1.5%