Exam FM: which formulas actually earn their keep

The formula sheet is longer than the exam

Interest theory looks enormous when you first meet it: annuities immediate and due, deferred and continuous, increasing and decreasing and geometric, loans, sinking funds, bonds, spot rates, forward rates, duration, convexity. Almost all of it collapses onto a handful of expressions, and the candidates who see that finish the exam with time to spare.

Tier one: learn these until they are reflexes

Four expressions carry an enormous share of the paper. If you know them cold and can move between them, most questions become bookkeeping.

• v = 1/(1+i) and d = i/(1+i) — every conversion question is one of these rearranged.
• aₙ = (1 − vⁿ)/i — and the fact that äₙ is just aₙ(1+i).
• P = L/aₙ for a loan payment, and Bₜ = P·a_(n−t) for the balance.
• P = Fr·aₙ + Cvⁿ for a bond price.

Tier two: the ones that turn a hard question into an easy one

These do not appear on every paper, but when they do they save several minutes each — and the alternative is summing a series by hand under time pressure.

• (Ia)ₙ = (äₙ − n·vⁿ)/i, and the check (Ia)ₙ + (Da)ₙ = (n+1)aₙ.
• The geometric annuity value (1 − ((1+g)/(1+i))ⁿ)/(i − g).
• 1/aₙ = i + 1/sₙ, the bridge between amortisation and sinking funds.
• D_Mod = D_Mac/(1+i), and ΔP/P ≈ −D_Mod·Δi.

Tier three: know what they are, look up the details

Makeham's formula, the callable-bond rules, convexity's exact expression and the swap rate formula are all worth recognising, but they reward understanding over memorisation. If you know that a swap rate is (1 − last discount factor) divided by the sum of the discount factors, you can rebuild it; memorising it as symbols without that sentence is fragile.

The discipline that beats memorisation

Every FM formula is a present value. When recall fails, write the cash flows on a time line and discount them one by one — slower, but never wrong. Candidates who practise that fallback can afford to forget a formula in the exam room; candidates who cannot are one memory lapse from losing a question they understood perfectly.