Verified solution · Exam FM

SOA Exam FM Sample Question #33 Solution

This Exam FM sample reference tests Principal Portion Progression. The first interest is 0.08(2,000) = 160, so principal is 603.85 − 160 = 443.85, or 444. The result agrees with the published answer key, 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 Principal Portion Progression question

Setup

Successive principal portions in a level-payment loan grow by 1 + i. The supplied later principal amount therefore determines the level payment R one period earlier.

R=559.12(1.08)=603.85

Model

After obtaining R = 603.85, value the four remaining payments at origination to recover the loan amount 2,000. First-period principal is payment less first-period interest.

L=Ra_{\overline4|\,0.08}=2000

Compute

The first interest is 0.08(2,000) = 160, so principal is 603.85 − 160 = 443.85, or 444.

P_1=R-0.08L=443.85

Answer

The calculation gives 444 for principal portion progression, matching published choice A.

\boxed{P_1=444\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 4 N; 8 I/Y; 603.85 +/- PMT; 0 FV; CPT PV2000.00This checks the reconstructed loan principal before splitting payment 1.

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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 (454) does not match the checked principal portion progression result (444); no distinct standard one-step error is identifiable.
CChoice C (464) does not match the checked principal portion progression result (444); no distinct standard one-step error is identifiable.
DChoice D (474) does not match the checked principal portion progression result (444); no distinct standard one-step error is identifiable.
EChoice E (484) does not match the checked principal portion progression result (444); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: later principal portion from the first amortization amount

The principal portion of the first annual payment on a level-payment loan is 400. The annual effective interest rate is 5%. Calculate the principal portion of payment 6.

A
459.46
B
484.99
C
510.51
D
536.04
E
561.56

Variant answer in brief

Accumulating 400 through five 5% steps gives 510.51. The sixth principal portion is 510.51, which is choice C.

Setup

Principal portions of a level-payment loan grow by the factor 1 + i from one payment to the next.

P_1=400,\quad i=0.05

Model

Payment 6 is five progression steps after payment 1.

P_k=P_1(1+i)^{k-1}

Compute

Accumulating 400 through five 5% steps gives 510.51.

P_6=400(1.05)^5=510.512625

Answer

The sixth principal portion is 510.51, which is choice C.

\boxed{P_6=510.51\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 #33 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Principal Portion Progression 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: later principal portion from the first amortization amount

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution