Verified solution · Exam FM

SOA Exam FM Sample Question #371 Solution

This Exam FM sample reference tests Interest Rate Valuation. Every quoted zero price implies the same annual effective yield of 6%, so yield does not vary with maturity and the curve is flat, choice B.

Independent analysis by ActuaryProof · reviewed August 4, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Interest Rate Valuation question

Setup

Convert each zero-coupon price into its maturity-specific spot yield.

y_n=\left(\frac{1000}{P_n}\right)^{1/n}-1

Model

The one- and five-year prices both produce 6% annual effective yields.

y_1=6.00\%,\qquad y_5=6.00\%

Compute

The ten- and twenty-year calculations give the same yield, so there is no maturity slope or curvature.

y_{10}=6.00\%,\qquad y_{20}=6.00\%

Answer

A constant spot yield across all terms is a flat yield curve, choice B.

\boxed{\text{flat yield curve}\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

2nd CLR TVM; 1 N; 943.40 +/- PV; 0 PMT; 1000 FV; CPT I/Y; repeat with N and PV equal to 5 and 747.26, 10 and 558.39, 20 and 311.80I/Y = 6.0000 for every maturityUse annual periods and preserve the negative sign on purchase price.

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AAn increasing curve would require longer-maturity spot yields above the one-year yield.
CAn inverted curve would require yields to decline with maturity, but all four are equal.
DNo upward curvature remains after converting prices to spot yields.
ENo downward curvature remains because the inferred yields are constant.

Original practice · fully worked

Original variant: price a zero from a stated flat curve

A market spot curve is flat at 5% effective annually. Determine the price of a seven-year zero-coupon security that pays 1,000 at maturity.

A
650.68
B
680.68
C
710.68
D
740.68
E
770.68

Variant answer in brief

Discounting 1,000 for seven years at the common 5% spot rate gives 710.68, choice C.

Setup

A flat curve supplies the same spot rate for the seven-year maturity.

P=1000(1.05)^{-7}

Model

A zero-coupon security has only its maturity payment to discount.

(1.05)^{-7}=0.7106813

Compute

The seven-year discount factor is 0.7106813.

P=710.6813

Answer

The security price is 710.68, corresponding to choice C.

\boxed{P=710.68\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 7 N; 5 I/Y; 0 PMT; 1000 FV; CPT PVPV = -710.68

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #371 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Interest Rate Valuation question

Setup

Model

Compute

Answer

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: price a zero from a stated flat curve

Variant answer in brief

Setup

Model

Compute

Answer

BA II Plus keystrokes

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution