Verified solution · Exam FM
This Exam FM sample reference tests Interest Rate Valuation. Nominal purchasing-power accumulation equals real accumulation times inflation accumulation, so 1 + i = (1 + i′)(1 + r) and i = i′ + r + i′r, choice B.
Independent solution
Setup
Separate growth in purchasing power from growth in the price level.
Model
The nominal accumulation factor is the product of the real and inflation factors.
Compute
Expanding the product and subtracting one retains the interaction term.
Answer
The nominal rate is i prime plus r plus their product, corresponding to choice B.
Continue without hunting through PDFs
The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
An investment earns 8% nominally while its real annual effective return is 3%. Determine the annual effective inflation rate.
Dividing the nominal factor 1.08 by the real factor 1.03 gives inflation 4.85%, choice C.
Setup
Use accumulation factors rather than subtracting percentage rates.
Model
Divide nominal growth by real growth to isolate price-level growth.
Compute
The resulting inflation rate is 0.0485437.
Answer
Annual effective inflation is 4.85%, corresponding to choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 51 Exam FM time value of money practice problems.
Continue in syllabus order
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam FM Sample Question #402 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
