SOA Exam ALTAM Sample Question 32

Study guide: Exam ALTAM

NED Life issues a fully discrete whole life insurance of 100,000 on (50) with a return of premium benefit subject to the following conditions:

If death occurs in the first 10 years, no premiums are returned.
If death occurs after 10 years, all premiums, including the first 10, are returned without interest at the end of the year of death.

You are given:

(i) The gross premium is 2,000.

(ii) Premium expenses, payable at the beginning of the year, are 80% of the first year's premium and 5% of premium in subsequent years.

(iii) Termination expenses of 1,000 are paid at the end of the year of death.

(iv) Mortality follows the Standard Ultimate Life Table.

(v) $i = 0.05$

(vi) $L^g$ is the gross loss at issue random variable.

(vii) $(IA)_{60} = 6.63303$

(viii) ${}_kV^g$ denotes the gross premium policy value at the end of year $k$ .

(Part (a), (b) and (c) are covered by the FAM-L exam.)

Part a (1 point)

Show that if $T_{50} = 11.8$ , then $L^g$ is 53,420 to the nearest 10. You should calculate the value to the nearest 1.

Part b (2 points)

Calculate $E[L^g]$ .

Part c (2 points)

Show that ${}_{10}V^g$ is 20,070 to the nearest 10. You should calculate the value to the nearest 1.

Part d (4 points)

NED Life had 1000 such policies in force at the end of 15 years. You are given:

(i) ${}_{15}V^g = 34{,}333.78$ and ${}_{16}V^g = 37{,}480.51$

(ii) During year 16:

There were 7 deaths.
i = 0.052
Premium expenses were 4% of premium.
Termination expenses were 2,000 per death.

(i) Calculate the total gain in the 16th year.

(ii) Calculate the gain by source in the following order: expenses (E), interest (I) and mortality (M).

Part e (1 point)

An actuary at NED Life was asked to calculate the gain by source. He wasn't sure which order to use, so he calculated the gain based on all six possible orders. Referring to the sources of gain in order by their first letters, the order you did in part (d) was EIM.

Without further calculation, state, using the three-letter ids, which, if any, of the other 5 orders had the same gain from interest as EIM. Justify your response.

(This is Question 1 from the Fall 2021 Form A Written Answer exam.)

Answer this question and see the worked solution