Verified solution · Exam FM

SOA Exam FM Sample Question #244 Solution

This Exam FM sample reference tests Annuities. Separate each payment into a level 110 component and an arithmetic increment component. Their factors at 10% are 8.51356 and 55.40691; solving the 2,000 price gives X = 19.19, 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

Write payment k as 110 plus k minus 1 copies of the increment.

P_k=110+(k-1)X

Model

Value the level and arithmetic-increase components separately.

2000=110a_{\overline{20}|0.10}+X\frac{a_{\overline{20}|0.10}-20v^{20}}{0.10}

Compute

The level component is 936.49 and the increment factor is 55.40691, so X = 19.1945.

X=\frac{2000-936.49200917}{55.40691159}=19.19450047

Answer

The annual payment increase is approximately 19.19, selecting choice C.

\boxed{X\approx19.19\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 (16.64) does not satisfy the 20-term arithmetic-increasing annuity present-value equation; no distinct standard one-step error is identifiable.
BChoice B (17.45) does not satisfy the 20-term arithmetic-increasing annuity present-value equation; no distinct standard one-step error is identifiable.
DChoice D (21.00) does not satisfy the 20-term arithmetic-increasing annuity present-value equation; no distinct standard one-step error is identifiable.
EChoice E (22.68) does not satisfy the 20-term arithmetic-increasing annuity present-value equation; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: price of a fixed arithmetic payment schedule

A training grant pays 100 at year 1 and then increases each annual payment by 20 for a total of eight payments. At a 6% annual effective yield, calculate the present value of the grant.

A
916.03
B
966.92
C
1,017.81
D
1,068.70
E
1,119.59

Variant answer in brief

Discounting the eight payments 100, 120, through 240 at 6% gives present value 1,017.81, choice C.

Setup

List the arithmetic payment rule over the eight year-end dates.

P_k=100+20(k-1),\qquad k=1,\ldots,8

Model

Discount each generated payment at the common 6% annual yield.

PV=\sum_{k=1}^{8}[100+20(k-1)](1.06)^{-k}

Compute

The direct eight-term sum is 1017.810995.

PV=1017.81099451

Answer

The grant's present value is 1,017.81, which is choice C.

\boxed{PV\approx1017.81\quad\text{(C)}}

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Turn this solution into a complete study sequence

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 #244 — 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: price of a fixed arithmetic payment schedule

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution