Verified solution · Exam FM

SOA Exam FM Sample Question #403 Solution

This Exam FM sample reference tests Annuities and Perpetuities. Fund X generates annual interest deposit 930.83; the five deposits accumulate in Fund Y as an annuity-immediate, and 5,461 = 930.83s₅ implies i = 8.00%, 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 Annuities and Perpetuities question

Setup

Compute the effective annual interest generated by Fund X's quarterly nominal quote.

C=10000\left[(1+0.09/4)^4-1\right]=930.83

Model

That same dollar interest is withdrawn and deposited into Fund Y at each year-end.

5461=Cs_{\overline{5}|\,i}

Compute

Five level deposits accumulated to the fifth deposit date determine Fund Y's annual rate.

s_{\overline{5}|\,i}=5.866\Longrightarrow i=0.08

Answer

The annual effective rate is 8.00%, corresponding to choice B.

\boxed{i=8.00\%\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

2nd CLR TVM; 5 N; 0 PV; 930.83 +/- PMT; 5461 FV; CPT I/YI/Y = 8.00

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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 is inconsistent with the annual interest-transfer amount and five-deposit accumulation equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the annual interest-transfer amount and five-deposit accumulation equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the annual interest-transfer amount and five-deposit accumulation equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the annual interest-transfer amount and five-deposit accumulation equation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: balance from reinvested annual interest withdrawals

Fund X holds 20,000 at 8% nominal convertible quarterly. At each year-end, all interest earned that year is moved to Fund Y, which earns 5% annually. Determine Fund Y's balance immediately after the fourth transfer.

A
6,105.86
B
6,605.86
C
7,105.86
D
7,605.86
E
8,105.86

Variant answer in brief

Each annual transfer is 1,648.64; four such transfers accumulated at 5% total 7,105.86, choice C.

Setup

Convert Fund X's nominal quote to its annual interest dollar amount.

C=20000\left[(1+0.08/4)^4-1\right]=1648.6432

Model

The year-end transfers form an accumulated annuity in Fund Y.

F_Y=Cs_{\overline{4}|\,0.05}

Compute

Four transfers at 5% grow to 7,105.8583 immediately after transfer four.

F_Y=7105.8583

Answer

Fund Y holds 7,105.86, corresponding to choice C.

\boxed{F_Y=7105.86\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 4 N; 5 I/Y; 0 PV; 1648.6432 +/- PMT; CPT FVFV = 7105.86

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #403 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities and Perpetuities question

Setup

Model

Compute

Answer

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: balance from reinvested annual interest withdrawals

Variant answer in brief

Setup

Model

Compute

Answer

BA II Plus keystrokes

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution