Actuarial Science LTAM

A deferred annuity on 30 will pay $4000 per month for life, starting at age 60. A single gross premium of $175,000 is paid at issue. The product is priced using 5% interest and SULT mortality with the two term Woolhouse approximation for annuities paid more frequently than annually. Expenses are 6% of the gross premium.

a) Find the expected present value at issue of the annuity benefits.

b) At age 60, the annuity may be exchanged for a different annuity with an equivalent expected present value. Find the monthly benefit payable for life with a 5-year guarantee starting at age 60 that has the same EPV as the life annuity paying $4000 per month for life.

c) The product pays a death benefit equal to the Gross Premium plus interest at 5% payable at the time of death. Find the expected present value of the death benefit.

d) Give an expression for the Gross Loss at Issue random variable L₀^g.

e) Find the expected present value of L₀^g.