Exam FM Annuity and Perpetuity Practice Problems

Technique orientation

What annuities and perpetuities questions are testing

An annuity formula is a compressed cash-flow diagram. Its value depends on the payment dates, the valuation date, and the effective rate per payment period—not on the label attached to the financial story. Write the first and last payment times before choosing an annuity-immediate, annuity-due, deferred, varying, or perpetuity factor.

Exam FM frequently changes payment frequency, growth pattern, or deferral while leaving the underlying equation of value familiar. Level streams can often be checked on a BA II Plus TVM worksheet; irregular or varying streams are safer as an explicit sum or cash-flow worksheet. In both cases, the analytic timeline controls the calculator inputs.

Recognition audit

Signals that this is the right method

A finite sequence of level payments starts one period after valuation or immediately at valuation.
The first payment is deferred, so the standard factor must be moved from its natural valuation date.
Payments increase arithmetically or geometrically and must be decomposed or valued as a varying stream.
Payments continue indefinitely, making convergence and the relationship between growth and interest essential.

Before calculation

A disciplined first pass

Name the requested quantity, mark its units or time point, and identify the assumption that permits the formula. Only then insert the numerical inputs. This separates model errors from arithmetic errors and makes the answer-choice comparison auditable.

Formula core

Annuities and Perpetuities formulas to know

These identities are starting points, not substitutes for checking support, timing, rate periods, or independence assumptions.

Level annuity-immediate

a_{\overline{n}|}=\frac{1-v^n}{i},\qquad s_{\overline{n}|}=\frac{(1+i)^n-1}{i},\qquad v=(1+i)^{-1}

The present-value factor sits one period before the first payment; the accumulated-value factor sits at the final payment date.

Annuity-due

\ddot{a}_{\overline{n}|}=(1+i)a_{\overline{n}|},\qquad \ddot{s}_{\overline{n}|}=(1+i)s_{\overline{n}|}

Moving every payment one period earlier multiplies present value by 1 + i.

Level and growing perpetuities

a_{\overline{\infty}|}=\frac{1}{i},\qquad PV_{\text{growing}}=\frac{P_1}{i-g}\quad(i>g)

P₁ is the payment one period after valuation; a payment at valuation must be handled separately.

Three failure modes to catch

Selecting annuity-immediate when the first payment occurs at the valuation date.
Discounting a deferred factor by the number of payments rather than by the number of periods before its natural valuation date.
Using an annual quoted rate directly when payments occur monthly, quarterly, or semiannually.

Verified practice ledger

Exam FM annuities and perpetuities problems and solutions

The list is grouped by current official syllabus area. Every link opens a step-labeled solution, verification artifact, distractor analysis, and one fully worked original variant.

Annuities and Non-contingent Cash Flows

54 verified references

Continue the study loop

Keep every worked reference in one searchable manual

The complete Exam FM manual includes all active sample-reference solutions, their wrong-choice analysis, and one independently written worked variant per reference. The free formula sheet is the compact companion for recall between practice sessions.

View contents and sample pagesGet the free formula sheet

Related drills

Other Exam FM technique collections

Switch techniques when you can identify the current method before writing a formula and can explain each wrong-choice mechanism.

49 verified problems

Annuities and Perpetuities practice problems