Verified solution · Exam FM

SOA Exam FM Sample Question #334 Solution

This Exam FM sample reference tests Accumulation into an Annuity-Due. The annuity-due requires 10698.97 at time 5. Equating this to 9550 accumulated for five years gives i = 2.2981%, which rounds to 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 Accumulation into an Annuity-Due question

Setup

Value the twenty annual due payments at the reinvestment date using 4%.

F_5=756.97\ddot a_{\overline{20}|0.04}=10{,}698.97

Model

The original deposit must grow to this amount over five years.

9{,}550(1+i)^5=10{,}698.97

Compute

Solve the five-year accumulation equation.

i=\left(\frac{10{,}698.97}{9{,}550}\right)^{1/5}-1=0.0229813

Answer

The annual effective rate is 2.3%, choice B.

\boxed{i\approx2.3\%\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

20 · N; 4 · I/Y; 756.97 · +/− · PMT; 0 · FV; BGN mode; CPT · PV10,698.97This is the amount required at time 5.

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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 treats the annuity as immediate, lowering the required time-5 fund.
CChoice C reports approximately the total five-year growth rather than its annualized rate.
DChoice D divides the fund increase by 9550 without taking a fifth root.
EChoice E uses the annuity's twenty-year horizon to annualize the original five-year accumulation.

Original practice · fully worked

Original variant: annuity payment supported by an accumulated deposit

A deposit of 12,000 earns 3% effective annually for six years. At that time the balance buys a ten-year annuity-due priced at 5% effective with annual payment A. Determine A.

A
1,512.40
B
1,643.88
C
1,767.26
D
1,855.70
E
2,003.11

Variant answer in brief

The deposit grows to 14328.63. Dividing by the ten-payment annuity-due factor at 5% gives A = 1767.26, choice C.

Setup

Accumulate the initial deposit to the annuity purchase date.

F=12{,}000(1.03)^6=14{,}328.6276

Model

The first annuity payment is immediate at that date.

F=A\ddot a_{\overline{10}|0.05}

Compute

Divide by the due factor.

A=\frac{14{,}328.6276}{\ddot a_{\overline{10}|0.05}}=1{,}767.2598

Answer

The annual payment is 1767.26, choice C.

\boxed{A=1{,}767.26\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #334 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Accumulation into an Annuity-Due 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: annuity payment supported by an accumulated deposit

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution