Verified solution · Exam FM

SOA Exam FM Sample Question #15 Solution

This Exam FM sample reference tests Increasing Annuity Present Value. Evaluation gives 2,729.7. The requested rounded present value is 2,730. The result agrees with the published answer key, 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 Increasing Annuity Present Value question

Setup

Convert the quoted quarterly rate to the effective rate j for each three-month payment interval. Sixty increasing payments of 2, 4, …, 120 are then valued at time 0.

(1+j)^3=1+0.09/4\Longrightarrow j=0.007444

Model

The payment stream is twice an increasing annuity-immediate, so its value is 2 times the standard increasing-annuity factor at j = 0.007444.

PV=2(Ia)_{\overline{60}|\,j}

Compute

Evaluation gives 2,729.7. The requested rounded present value is 2,730.

PV=2729.7

Answer

The calculation gives 2730 for increasing annuity present value, matching published choice B.

\boxed{PV=2730\quad\text{(B)}}

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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 (2680) does not match the checked increasing annuity present value result (2730); no distinct standard one-step error is identifiable.
CChoice C (2780) does not match the checked increasing annuity present value result (2730); no distinct standard one-step error is identifiable.
DChoice D (2830) does not match the checked increasing annuity present value result (2730); no distinct standard one-step error is identifiable.
EChoice E (2880) does not match the checked increasing annuity present value result (2730); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: one-year increasing monthly rewards

A reward plan pays 10 after one month, 20 after two months, and continues increasing by 10 through month 12. At 1% monthly interest, find its present value.

A
680.00
B
700.00
C
718.24
D
735.00
E
760.00

Variant answer in brief

Evaluation gives 718.2375, or 718.24. This selects choice C.

Setup

The twelve month-end rewards are 10, 20, …, 120 and the monthly yield is 1%.

PV=\sum_{t=1}^{12}10t(1.01)^{-t}

Model

Their present value is ten times the standard twelve-period increasing annuity-immediate.

PV=10(Ia)_{\overline{12}|\,0.01}

Compute

Evaluation gives 718.2375, or 718.24.

PV=718.2375

Answer

The requested value is 718.24, so the correct choice is C.

\boxed{PV=718.24\quad\text{(C)}}

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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 #15 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Increasing Annuity Present Value question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: one-year increasing monthly rewards

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution