Verified solution · Exam FM

SOA Exam FM Sample Question #283 Solution

This Exam FM sample reference tests Spot and Forward Rates. Paul's two-year yield is 9.5445%. The combined 10% terminal-value equation implies Toby receives Z = 236.00, and Toby's own cash-flow equation gives yield 11.5549%. The difference is 2.01%, choice C.

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 Spot and Forward Rates question

Setup

Solve Paul's two-year yield from his single investment and receipt.

500(1+X)^2=600

Model

Use the combined 10% terminal-value equation to determine Toby's final receipt.

600(1.10)^2+100(1.10)=600+Z

Compute

This gives Z = 236.00. Solving Toby's two-deposit equation gives Y = 11.554944% and Y − X = 2.0104%.

100(1+Y)^2+100(1+Y)=Z

Y-X=0.0201043271

Answer

The yield difference is approximately 2%, selecting choice C.

\boxed{Y-X\approx2\%\quad\text{(C)}}

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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.

AChoice A (0%) does not satisfy the individual terminal-value equations and the combined 10% terminal wealth; no distinct standard one-step error is identifiable.
BChoice B (1%) does not satisfy the individual terminal-value equations and the combined 10% terminal wealth; no distinct standard one-step error is identifiable.
DChoice D (3%) does not satisfy the individual terminal-value equations and the combined 10% terminal wealth; no distinct standard one-step error is identifiable.
EChoice E (4%) does not satisfy the individual terminal-value equations and the combined 10% terminal wealth; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: combined portfolio yield from two distinct investor cash-flow patterns

Investor A deposits 400 today and receives 500 at year 2. Investor B deposits 100 today and another 100 at year 1, then receives 230 at year 2. Calculate the annual effective yield on the combined cash flows.

A
10.12%
B
10.68%
C
11.24%
D
11.81%
E
12.37%

Variant answer in brief

At year 2, the combined receipts are 730. Equating that to the accumulated 500 initial deposit plus the year-1 deposit gives annual effective yield 11.24%, choice C.

Setup

Combine cash flows at each date rather than averaging individual yields.

C_0=-500

C_1=-100

C_2=730

Model

Use year 2 as the comparison date for the combined investment.

500(1+j)^2+100(1+j)=730

Compute

The positive root is j = 11.243557%.

j=0.1124355653

Answer

The combined annual effective yield is 11.24%, selecting choice C.

\boxed{j\approx11.24\%\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #283 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Spot and Forward Rates question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: combined portfolio yield from two distinct investor cash-flow patterns

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution