Verified solution · Exam FM

SOA Exam FM Sample Question #277 Solution

This Exam FM sample reference tests Annuities. At year 15, the first deposit has 14 years of 8% growth and each later deposit has one fewer. Summing the growing deposits produces factor 32.284034, so X = 61.95, 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 Annuities question

Setup

Deposit k has amount X times 1.03 to the k minus 1 and accumulates from year k to year 15.

D_k=X(1.03)^{k-1}

F_{15}=\sum_{k=1}^{15}D_k(1.08)^{15-k}

Model

Factor out X from the finite geometric accumulation sum.

2000=X\sum_{k=1}^{15}(1.03)^{k-1}(1.08)^{15-k}

Compute

The accumulation factor is 32.28403395, giving X = 61.950127.

X=61.95012689

Answer

The first deposit is approximately 62, selecting choice C.

\boxed{X\approx62\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 (45) does not satisfy the time-15 sum of all fifteen growing deposits at their actual accumulation periods; no distinct standard one-step error is identifiable.
BChoice B (57) does not satisfy the time-15 sum of all fifteen growing deposits at their actual accumulation periods; no distinct standard one-step error is identifiable.
DChoice D (67) does not satisfy the time-15 sum of all fifteen growing deposits at their actual accumulation periods; no distinct standard one-step error is identifiable.
EChoice E (88) does not satisfy the time-15 sum of all fifteen growing deposits at their actual accumulation periods; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: deposit growth rate inferred from a terminal fund

A saver deposits 100 at year 1 and makes nine further year-end deposits, each growing by the same rate g. The account earns 6% annually. The fund immediately after the year-10 deposit is 1429.63. Calculate g.

A
1.60%
B
1.70%
C
1.80%
D
1.90%
E
2.00%

Variant answer in brief

Equating the ten accumulated deposits to the quoted year-10 fund and solving the geometric sum gives growth rate 2.00%, choice E.

Setup

Write deposit k and its accumulation to year 10.

D_k=100(1+g)^{k-1}

F_{10}=\sum_{k=1}^{10}D_k(1.06)^{10-k}

Model

Set that finite sum equal to the quoted terminal fund.

1429.63=100\sum_{k=1}^{10}(1+g)^{k-1}(1.06)^{10-k}

Compute

The relevant root is g = 2.000000%.

g=0.0200000000

Answer

The annual deposit growth rate is 2.00%, selecting choice E.

\boxed{g=2.00\%\quad\text{(E)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #277 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: deposit growth rate inferred from a terminal fund

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution