A life office sells an annuity to a man aged 70, for a single premium of P. The payments to him are $20,000 per year, payable monthly in advance. After his death a reduced widows pension of $12,000 per year will be paid to his wife, now aged 66, provided she is then alive. The payments are guaranteed (at the initial level) for the first 5 years. Initial expenses are $250, and there is an administrative cost of $8 associated with each monthly payment. Both lives are subject to the mortality of the PMA92/PFA92 ultimate table, and the interest basis is 4% per annum. Calculate the single premium P