Verified solution · Exam FM

SOA Exam FM Sample Question #361 Solution

This Exam FM sample reference tests Monthly Contributions Funding an Annual Perpetuity. At time 5 the annual perpetuity-due costs 44424.39, using the annual rate equivalent to 1% monthly. Sixty month-end contributions accumulate by factor 81.66967, so X = 543.95 and choice D.

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 Monthly Contributions Funding an Annual Perpetuity question

Setup

Convert the 1% monthly rate to an annual effective rate.

i_a=(1.01)^{12}-1=0.12682503

Model

The first perpetuity payment coincides with the last contribution, so value a perpetuity-due at time 5.

F_5=5{,}000\frac{1+i_a}{i_a}=44{,}424.3943

Compute

Accumulate sixty month-end contributions to that same time.

Xs_{\overline{60}|0.01}=44{,}424.3943

s_{\overline{60}|0.01}=81.6696699

Answer

The monthly contribution is 543.95, choice D.

\boxed{X=543.9522\approx544\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

60 · N; 1 · I/Y; 0 · PV; 44424.3943 · +/− · FV; CPT · PMT543.95END mode matches contributions at month-ends.

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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 values the annual perpetuity at a nominal 12% rate and delays its first payment.
BChoice B converts monthly to annual yield but prices a perpetuity-immediate at time 5.
CChoice C omits the sixtieth contribution that occurs at the purchase date.
EChoice E treats contributions as beginning-of-month and also advances the first perpetuity payment.

Original practice · fully worked

Original variant: perpetuity payment supported by monthly savings

A saver contributes 300 at each month-end for five years to an account earning 1% per month. Immediately after the final contribution, the balance purchases an annual perpetuity-due valued at the annual effective rate equivalent to 1% monthly. Determine its annual payment.

A
2,401.18
B
2,575.42
C
2,757.60
D
2,936.84
E
3,105.21

Variant answer in brief

The sixty contributions accumulate to 24500.90. Multiplying by the annual perpetuity-due payout rate gives annual payment 2757.60, choice C.

Setup

Accumulate the sixty month-end deposits.

F=300s_{\overline{60}|0.01}=24{,}500.9010

Model

Convert the monthly rate to its annual effective equivalent.

i_a=(1.01)^{12}-1=0.12682503

Compute

A perpetuity-due price is payment times one plus yield divided by yield.

A=F\frac{i_a}{1+i_a}=2{,}757.5954

Answer

The annual payment is 2757.60, choice C.

\boxed{A=2{,}757.60\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

60 · N; 1 · I/Y; 0 · PV; 300 · +/− · PMT; CPT · FV24,500.90Accumulated fund after the final contribution.

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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.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #361 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Monthly Contributions Funding an Annual Perpetuity 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: perpetuity payment supported by monthly savings

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