Actuarial Math Basics: Life Tables, Annuities & Premiums

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn a nominal monthly rate into an effective annual rate, work out the discount factor v and the discount rate d, and build a table of discount factors v^n for 10 years.
• Value 10 yearly payments of USD 12,000 as an annuity-immediate and an annuity-due, and find their accumulated value after 10 years.
• From the survivors lx of a life table you calculate deaths dx, the mortality rate qx, the survival rate px and the survival probability from age 60, then chart how mortality rises with age.
• Calculate the survival probabilities of an 85-year-old year by year, add them up to the curtate life expectancy e85 and compare it with e95.
• For a 60-year-old and a sum insured of USD 100,000 you calculate the expected present value of a 10-year term insurance, a 10-year pure endowment and their sum, the endowment insurance.
• Value a 10-year temporary life annuity-due of USD 12,000 a year for a 60-year-old and compare it with the annuity certain from lab 2.
• Set the annual premium for the 10-year endowment insurance so that the present value of the premiums equals the present value of the benefits, and compare it with a term-only premium.
• Calculate the net premium reserve of the endowment policy for every year, check year 5 with the prospective formula and chart how the reserve grows to the sum insured.