Verified solution · Exam FM

SOA Exam FM Sample Question #5 Solution

This Exam FM sample reference tests Accumulation of Transferred Cash Flows. The decreasing transfers accumulate to 565.38 and the level transfers to 1,519.29. Their sum is 2,084.67, which rounds to 2,085. The result agrees with the published answer key, 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 Accumulation of Transferred Cash Flows question

Setup

Separate the final fund into the accumulated regular transfers and the accumulated portions of interest that were also moved. This prevents the decreasing interest withdrawals from being mistaken for a level annuity.

\text{interest withdrawals}=6,5.4,\ldots,0.6

Model

The ten regular transfers form an accumulated-value annuity. The interest transfers decrease by 0.6 each period, so their time-10 value is represented by the decreasing-annuity accumulation term in the displayed equation.

A=6(Ds)_{\overline{10}|\,0.09}+100s_{\overline{10}|\,0.09}

Compute

The decreasing transfers accumulate to 565.38 and the level transfers to 1,519.29. Their sum is 2,084.67, which rounds to 2,085.

A=565.38+1519.29=2084.67

Answer

The calculation gives 2085 for accumulation of transferred cash flows, matching published choice C.

\boxed{A=2085\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 (1519) does not match the checked accumulation of transferred cash flows result (2085); no distinct standard one-step error is identifiable.
BChoice B (1819) does not match the checked accumulation of transferred cash flows result (2085); no distinct standard one-step error is identifiable.
DChoice D (2273) does not match the checked accumulation of transferred cash flows result (2085); no distinct standard one-step error is identifiable.
EChoice E (2431) does not match the checked accumulation of transferred cash flows result (2085); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: annual transfer reserve

A reserve receives 100 at the end of every year for ten years and earns 5% annually. Find the reserve balance immediately after the tenth transfer.

A
1200.00
B
1230.50
C
1250.00
D
1257.79
E
1300.00

Variant answer in brief

The reserve reaches 1,257.7893, hence 1,257.79. This selects choice D.

Setup

Each year-end transfer earns interest from its deposit date to time 10, so the cash flows form an annuity-immediate accumulation.

A=100s_{\overline{10}|\,0.05}

Model

Use the ten-period accumulated-value factor at 5% and multiply by the 100 transfer.

s_{\overline{10}|}=\frac{1.05^{10}-1}{0.05}

Compute

The reserve reaches 1,257.7893, hence 1,257.79.

A=1257.7893

Answer

The requested value is 1257.79, so the correct choice is D.

\boxed{A=1257.79\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 10 N; 5 I/Y; 0 PV; 100 +/- PMT; CPT FV1257.79END mode.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #5 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Accumulation of Transferred Cash Flows question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: annual transfer reserve

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