Verified solution · Exam FM

SOA Exam FM Sample Question #321 Solution

This Exam FM sample reference tests Mixed Interest-Rate Regimes. The three accumulation blocks are 12 quarters at 1%, three years at force 5%, and eight half-years at discount rate 3%. Their product grows 1000 to 1670.42, so choice C is correct.

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 Mixed Interest-Rate Regimes question

Setup

Convert each quoted regime to the accumulation form that matches its conversion period.

j_q=0.04/4=0.01

\delta=0.05

d_{1/2}=0.06/2=0.03

Model

Apply the regimes consecutively for three, three, and four years.

A_{10}=1{,}000(1.01)^{12}e^{0.05(3)}(1-0.03)^{-8}

Compute

The three factors compound to 1.67042424.

A_{10}=1{,}670.42424

Answer

The account contains approximately 1670, which is choice C.

\boxed{1{,}670\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 treats the final nominal discount rate as a nominal interest rate and uses 1.03 instead of the reciprocal of 0.97.
BChoice B rounds each of the three regime factors before multiplying them, losing several dollars over ten years.
DChoice D applies the 5% force for four years and the discount regime for only three years.
EChoice E converts the 6% nominal discount rate to a 6% effective annual interest rate.

Original practice · fully worked

Original variant: initial deposit for a target under three regimes

An account must contain 5,000 after seven years. It earns a nominal 6% rate convertible monthly for two years, a constant force of 4% for two years, and a nominal discount rate of 4% convertible quarterly for the final three years. Determine the required initial deposit.

A
3,418.21
B
3,512.87
C
3,588.40
D
3,629.64
E
3,774.09

Variant answer in brief

The seven-year accumulation factor is 1.37754789. Dividing the 5000 target by this factor gives an initial deposit of 3629.64, choice D.

Setup

Translate the three regimes into monthly, continuous, and quarterly factors.

j_m=0.06/12

d_q=0.04/4

Model

Accumulate one initial dollar through all seven years.

A=(1.005)^{24}e^{0.04(2)}(1-0.01)^{-12}

Compute

The factor is 1.37754789, so solve for the initial principal P.

P=\frac{5{,}000}{1.37754789}=3{,}629.638

Answer

The required deposit is 3629.64, choice D.

\boxed{P=3{,}629.64\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #321 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Mixed Interest-Rate Regimes question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: initial deposit for a target under three regimes

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution