Verified solution · Exam FM

SOA Exam FM Sample Question #366 Solution

This Exam FM sample reference tests Deposits Accumulated into a Semiannual Perpetuity. Accumulating the five beginning-year deposits to year 10 gives 1703.81. The half-year rate equivalent to 12% annually is 5.8301%, so the perpetuity-immediate payment is 99.33, 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 Deposits Accumulated into a Semiannual Perpetuity question

Setup

Place the beginning-year deposits at times zero through four and accumulate each to time 10.

F_{10}=100(1.13)^{10}+100(1.13)^9+150(1.13)^8+150(1.13)^7+150(1.13)^6

Model

The accumulated fund is 1703.8111.

F_{10}=1{,}703.8111

Compute

Convert the annual effective yield to a half-year effective rate and price a perpetuity-immediate.

j=(1.12)^{1/2}-1=0.05830052

F_{10}=\frac Xj

Answer

The semiannual payment is approximately 99, choice A.

X=1{,}703.8111(0.05830052)=99.3331

\boxed{X\approx99\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 divides 12% by two instead of using the exact half-year rate equivalent to 12% effective.
CChoice C delays all deposits by one year before accumulating them.
DChoice D uses 12% as the half-year perpetuity rate.
EChoice E treats the perpetuity as due and then doubles its semiannual payment.

Original practice · fully worked

Original variant: scale deposits to buy a target perpetuity

Deposits of 100q, 150q, and 200q are made at times 0, 1, and 2 into a fund earning 8% annually. At time 6 the fund buys a perpetuity-immediate paying 120 every half-year, valued at a 10% annual effective yield. Determine q.

A
3.20
B
3.48
C
3.78
D
4.05
E
4.32

Variant answer in brief

The perpetuity requires 2458.57 at time 6, while the unscaled deposits accumulate to 651.18. Their ratio is q = 3.7755, choice C.

Setup

Find the half-year rate and the fund required for the perpetuity.

j=(1.10)^{1/2}-1

F_6=\frac{120}{j}=2{,}458.5706

Model

Accumulate one unit of the stated deposit pattern to time 6.

B=100(1.08)^6+150(1.08)^5+200(1.08)^4=651.1844

Compute

The actual accumulated deposits equal q times this base value.

qB=F_6

q=\frac{2{,}458.5706}{651.1844}=3.7755365

Answer

The deposit scale is 3.78, choice C.

\boxed{q\approx3.78\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #366 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Deposits Accumulated into a Semiannual Perpetuity question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: scale deposits to buy a target perpetuity

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution