Exam FM practice problems: Increasing, decreasing and geometric annuities

10 problems · Untimed · Worked solution after each answer

Arithmetic increasing and decreasing annuities and perpetuities, geometric annuities and other non-level cash flows. This drill covers topic 2 of the Exam FM syllabus, Annuities and cash flows with non-contingent payments (20–30% of the exam).

2b Annuity present and accumulated values

Line drawing of a row of coin stacks, each taller than the one before, like a staircase

Before you start

Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Increasing, decreasing and geometric annuities

(Ia)ₙ⌉ = (äₙ⌉ − nvⁿ)/i and (Da)ₙ⌉ = (n − aₙ⌉)/i; a payment pattern P, P + Q, … is P·aₙ⌉ + Q·(aₙ⌉ − nvⁿ)/i.
An increasing perpetuity-immediate paying 1, 2, 3, … is worth 1/i + 1/i².
A geometric annuity-immediate growing at rate g is worth [1 − ((1 + g)/(1 + i))ⁿ]/(i − g); when g = i, it is n/(1 + i).
Split an irregular stream into a level part and a varying part, or value each block separately and discount it back.

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Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).