Bertha, aged 40, wishes to purchase an annuity. She is offered two equivalent plans:

(a) 500 per month for life, with 300 continuing to her husband after her death.

(b) 600 per month for life, with 150 continuing to her husband after her death.

Given d\Q = 31, and that the first payment under either plan will be made immediately, fmd the present value of the benefits payable to Bertha and her husband.