IIQE Paper 3 Life Insurance Procedures question: dies in the fifth policy year

IIQE Paper 3Life Insurance Procedures

A 15-year endowment for HK$300,000 is accepted with a debt of HK$140,000, falling by HK$10,000 at the end of each policy year for the first 14 years. If the life insured dies in the fifth policy year, the amount payable (ignoring bonuses) is:

A HK$160,000
B HK$190,000
C HK$200,000
D HK$210,000

Show the answer and explanation

Answer: C. HK$200,000

Answer: HK$200,000. By the fifth policy year the debt has been reduced at the end of years 1 to 4: HK$140,000 - (4 x HK$10,000) = HK$100,000. The amount payable is HK$300,000 - HK$100,000 = HK$200,000.Why not the others:• HK$160,000: This deducts the full starting debt of HK$140,000, ignoring the four reductions already made.• HK$190,000: This allows only three reductions; the debt falls at the end of each of years 1 to 4 before the fifth year begins.• HK$210,000: This allows five reductions; the fifth reduction happens only at the end of the fifth year.Watch out: Counting the reductions wrongly: a death in year n sees n - 1 reductions.Rule: Decreasing debt: amount payable = sum assured - outstanding debt; the debt falls by the stated step at the end of each year until it disappears.Source: IA Long Term Insurance (Paper III) Study Notes, 2022 Edition (8th ed., June 2022; for exams from 24 Oct 2022), 5.3.3(c)(i), p. 5/48