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ACT247

1 Question

You are given:

❼ px+t = 0.9 for 0 ≤ t ≤ 3.

❼ i = 8%.

Calculate 2¨ax:3|.

2 Question

Assuming that mortality follows the LTAM Select and Ultimate life table, and i = 5%, calculate the APV of a 10-year temporary annuity-immediate that pays $1 annually issued to a 50-year-old.

3 Question

Bob, aged 45, got injured and was awarded a structured settlement in the form of a pure endowment of $200, 000 to be paid when he turns 65 (should he survive). Bob’s original force of mortality was µxSULT and is based on the mortality assumptions in the LTAM standard ultimate life table. After the injury, it is assumed that µx = µxSULT+0.02. The force of interest is assumed to be 0.045. What is the APV of the structured settlement to the nearest dollar?

4 Question

Alice, 20 years of age, just bought a whole life annuity-due of $1 per year, payable annually, deferred for 20 years. Assuming that mortality follows the LTAM standard ultimate life table and i = 5%, calculate the single net pre-mium of the annuity.

5 Question

Let Yx,n be the present value of an n-year term continuous annuity of $1 per year for an insured aged x. Let Yx be the present value of a whole life continuous annuity of $1 per year for an insured aged x. Given a constant force of interest, δ, show that: