Verified solution · Exam FM

SOA Exam FM Sample Question #169 Solution

This Exam FM sample reference tests Annuities and Perpetuities. The effective monthly rate is 0.52617%; accumulating the level 1,097 component and the five-per-month increasing component for 180 months gives 442,031, 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.

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Independent solution

How to solve this Annuities and Perpetuities question

Setup

Only the first 180 monthly payments are accumulated, and the first of those is 1,102.

j=1.065^{1/12}-1=0.0052617

Model

Rewrite payment k as a level 1,097 plus an increasing component 5k.

A_{180}=1097s_{\overline{180}|\,j}+5(Is)_{\overline{180}|\,j}

Compute

At the monthly rate equivalent to 6.5%, the two accumulated components total 442,031.

A_{180}=327710+114321=442031

Answer

The accumulated value after 15 years is 442,031, which is choice A.

\boxed{A_{180}=442031\quad\text{(A)}}

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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.

BChoice B is inconsistent with the level-plus-increasing monthly accumulation over 180 payments; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the level-plus-increasing monthly accumulation over 180 payments; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the level-plus-increasing monthly accumulation over 180 payments; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the level-plus-increasing monthly accumulation over 180 payments; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: accumulated escalating community-garden dues

A community garden contributes 200 at the end of year 1, then raises each annual contribution by 20 through year 15. At 7% effective annually, calculate the fund immediately after the year-15 contribution.

A
7,000.00
B
7,500.00
C
7,919.81
D
8,300.00
E
8,700.00

Variant answer in brief

Accumulating the 15 arithmetic payments to year 15 gives 7,919.81, choice C.

Setup

Contribution k equals 200 plus 20 times k minus one and accumulates for 15 minus k years.

A_{15}=\sum_{k=1}^{15}[200+20(k-1)](1.07)^{15-k}

Model

Separate the level 200 stream from the arithmetic step component.

A_{15}=200s_{\overline{15}|\,0.07}+20(Ds)_{\overline{15}|\,0.07}

Compute

Evaluating both accumulated annuity parts at 7% gives 7,919.8107.

A_{15}=7919.8107

Answer

The year-15 fund is 7,919.81, which is choice C.

\boxed{A_{15}=7919.81\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #169 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities and Perpetuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: accumulated escalating community-garden dues

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution