for number one do we divide the rate by 2 bevause it says semiannual?

and for the second problem why do we divide the sum by (1.03)^2? when it has a one year maturity? shouldnt we divide by 1.06?

8. For the two-period (each period is 6 months) binomial option pricing model, S0=50, Su, and the annual interest rate with semiannual compounding is 6%. =52.5, andSd=48.0Calculate the probability (p) and the stock price moving up in one time step?( a) 0.5555(b) 0.6666(c) 0.7777"(d) 0.8888(e) Cannot be calculated. T = interest rate per period = semi annual interest rate = 6%/2 = 3% D = [S0 x (1 + r) - Sd] / (Su-Sd) = [50 x (1 + 3%) - 48]/(52.5 - 48) = 0.7778 = 0.7728 OR 50X (1.03)-48 (32.5-48) 10. Continuing the previous 2 problems, what is the value of a call option with strike price $50 and time-to-maturity = 1 year.(a) $3.24(b) $3.14(c) $3.06(d) $3.05*(e) $3.00 u = Su/S0 = 62.5/50 = 1.05; d = Sd/S0 = 48/50 = 0.96 $2.5160 = 1.05;d OR: 0.1716% 5.125+ 2 x 0.7776 *(1-07778 Suu = u x Su = 1.05 x 52.5 = 55.125 Sum X 0.40 to Sud = Su x d = 52.5 x 0.96 = 52.5x0.96 Sdd = d * Sd = 0.96 x 48 = 46.08 - Sad Cuu = max (Suu - K, 0) = max (56.125 - 50,0) = 5.125 : 50.40 sud (1.03)2 su = $3.05 su .525 -53.125 so 50 sogged 50x105 xlios - 55.125 Cud = max (Sud - K, 0) = max (50.40 - 50,0) = 0.40 Sod Cdd = max (Sdd - K, 0) = max(46.08 - 50,0) = 0 5048 52. x0.96 Sa Hence, the value of the call option = [p2 x Cu + 2p(1-P) x Cud + (1 - p)-Cdd]/(1 + ) = [0.77782 x 5.125 + 2 x 0.7778 x (1 - 0.7778) X 0.40 +0]/(1+3%) = $3.05. 46.08 sad 48x0.96= 46.08 . p Cud