You are given q₆₀ =0.20, q₆₁ =0.25, q₆₂ =0.40, q₆₃ =0.50. The interest rate is a constant 5% for the first 2 years, and 7% after that. A 5 year life annuity on (60) provides for payments of 100(1+k) at time k, where k=0,1,2,3,4.

(a) Find the present value.

(b) Suppose that instead of being a straight life annuity, the first three annuity payments are guaranteed regardless of whether (60) is alive or not. Find the present value now.