Actuarial

Find the following assuming 5% interest, and SULT mortality.

a) Find the following expected present values of the following annuities assuming that deaths are uniformly distributed across integer ages.

i) An annuity due paying $20,000 per quarter while [39] survives to a maximum of 20 years.

ii) A life annuity on [72] paying continuously at the rate of $25,000 per year.

b) Find the expected present value of a life annuity immediate on [58] paying $2500 per month:

i) using the 2-term Woolhouse approximation.

ii) using the 3-term Woolhouse approximation