Verified solution · Exam FM

SOA Exam FM Sample Question #16 Solution

This Exam FM sample reference tests Equivalent Cash-Flow Streams. The implied annual effective rate satisfies (1 + i)¹⁰ = 1/0.7088. Taking the tenth root gives i = 0.03501, or 3.5%. The result agrees with the published answer key, choice A.

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.

Read the solution Open official source

Independent solution

How to solve this Equivalent Cash-Flow Streams question

Setup

Use one n-period block as the timing unit. The supplied relation gives vⁿ = 0.76, so the three earlier cash flows have time-0 values 100, 200(0.76), and 300(0.76)².

100+200(0.76)+300(0.76)^2=600v^{10}

Model

Their total must equal the time-0 value of the single payment at time 10n. This produces 600v¹⁰ⁿ = 425.28, or v¹⁰ⁿ = 0.7088.

v^{10}=0.7088

Compute

The implied annual effective rate satisfies (1 + i)¹⁰ = 1/0.7088. Taking the tenth root gives i = 0.03501, or 3.5%.

i=0.7088^{-1/10}-1=0.03501

Answer

The calculation gives 3.5% for equivalent cash-flow streams, matching published choice A.

\boxed{i=3.5\%\quad\text{(A)}}

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

Error diagnosis

Why the other letters tempt

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

BChoice B (4.0%) does not match the checked equivalent cash-flow streams result (3.5%); no distinct standard one-step error is identifiable.
CChoice C (4.5%) does not match the checked equivalent cash-flow streams result (3.5%); no distinct standard one-step error is identifiable.
DChoice D (5.0%) does not match the checked equivalent cash-flow streams result (3.5%); no distinct standard one-step error is identifiable.
EChoice E (5.5%) does not match the checked equivalent cash-flow streams result (3.5%); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: matching a dated lump sum

A stream pays 50 now, 100 at time n, and 150 at time 2n, where vⁿ=0.80. It is equivalent to 300 at time 6. Find the annual effective rate.

A
4.00%
B
4.50%
C
4.83%
D
5.00%
E
5.25%

Variant answer in brief

Solving 226 = 300v⁶ gives i = 0.04833995, or 4.83%. This selects choice C.

Setup

Use the supplied block discount factor 0.8 to value the three early payments at time 0.

50+100(0.8)+150(0.8)^2=226

Model

The total 226 must equal the time-0 value of 300 paid after six years.

226=300v^6

Compute

Solving 226 = 300v⁶ gives i = 0.04833995, or 4.83%.

i=(300/226)^{1/6}-1=0.04834

Answer

The requested value is 4.83%, so the correct choice is C.

\boxed{i=4.83\%\quad\text{(C)}}

Keep practicing

Turn this solution into a complete study sequence

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.

See the Exam FM study manual PDF — $49 More Exam FM Time Value of Money practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #16 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Equivalent Cash-Flow Streams question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: matching a dated lump sum

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution