Tommy is examining some risk-free Singapore government securities. The yields to maturity on three government bonds with maturities of 1, 2 and 3 years are respectively 3%, 4% and 6%. The bonds all pay an annual coupon and have the same coupon rate of 1% and a face value of $1,000. 

(a) Calculate the prices of the three (3) bonds.  

(b) (i) Calculate the expected 1-year interest rate for year 2. 

(ii) Calculate the expected 1-year interest rate for year 3