actuarial mathematics

Question 2 (a) A deferred annuity is issued to two (2) lives (30) and (40). Payments will begin on the fifth anniversary provided at least one of the two is alive then. The annuity will thereafter pay i) If both are still alive on the 5th anniversary, $30,000 per annum while both are still alive and reducing to $15,000.00 on the first death. The $15,000.00 will continue throughout the lifetime of the last survivor. ii) If only one is alive on the 5th anniversary, $15,000.00 per annum throughout life. Calculate the AVP of these benefits assuming that both lives are independently subject to mortality of the Tables with i = 6% p.a.e