Verified solution · Exam FM

SOA Exam FM Sample Question #360 Solution

This Exam FM sample reference tests Monthly Perpetuity with Annual Step Growth. The first twelve monthly payments are worth 5756.43 at the exact monthly rate. Treating each twelve-payment block as an annual unit growing 5% while discounting 8% gives total value 207231.44, choice D.

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 Monthly Perpetuity with Annual Step Growth question

Setup

Convert the annual effective yield to its equivalent monthly rate and price the first twelve-payment block.

j=1.08^{1/12}-1

B=500a_{\overline{12}|j}=5{,}756.4289

Model

Each later block is one year farther away and 5% larger.

PV=B\sum_{k=0}^{\infty}\left(\frac{1.05}{1.08}\right)^k

Compute

Evaluate the geometric block series.

PV=\frac{5{,}756.4289}{1-1.05/1.08}=207{,}231.4413

Answer

The perpetuity value is approximately 207231, choice D.

\boxed{PV\approx207{,}231\quad\text{(D)}}

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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 values the monthly stream at a nominal monthly rate obtained by dividing 8% by twelve.
BChoice B delays the first twelve-payment block by one full year.
CChoice C treats the annual 5% increase as a monthly increase within every block.
EChoice E advances each annual block to the beginning of its year even though its payments occur monthly.

Original practice · fully worked

Original variant: growth rate implied by a perpetuity price

A monthly perpetuity pays 400 for the first twelve months. At the start of each later twelve-payment block, the monthly amount increases by annual rate g. Its present value is 100,000 at a 6% annual effective yield. Determine g.

A
0.50%
B
0.82%
C
1.07%
D
1.35%
E
1.60%

Variant answer in brief

The first monthly block is worth 4651.52. Solving the geometric block-price equation gives annual step growth 1.0694%, choice C.

Setup

Price the first twelve payments at the exact monthly equivalent of 6%.

j=1.06^{1/12}-1

B=400a_{\overline{12}|j}=4{,}651.5201

Model

Successive block values form a geometric series with ratio one plus g divided by 1.06.

100{,}000=\frac{B}{1-(1+g)/1.06}

Compute

Rearrange for the annual step growth.

g=1.06\left(1-\frac{B}{100{,}000}\right)-1=0.0106939

Answer

The block growth rate is 1.07%, choice C.

\boxed{g\approx1.07\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #360 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Monthly Perpetuity with Annual Step Growth question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: growth rate implied by a perpetuity price

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution