Verified solution · Exam FM

SOA Exam FM Sample Question #232 Solution

This Exam FM sample reference tests Loan Balances and Amortization. At the beginning of year 7, six payments have been made. Accumulating the original loan for six years and subtracting the accumulated value of those payments gives balance 3659.90, so choice B 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 Loan Balances and Amortization question

Setup

The requested date is immediately after the sixth year-end payment.

t=6

Model

Use the retrospective balance: accumulated principal minus the accumulated value of payments already made.

B_6=4000(1.05)^6-250s_{\overline6|0.05}

Compute

The accumulated principal is 5360.38 and the six payments accumulate to 1700.48, leaving 3659.90.

B_6=3659.904359

Answer

The outstanding balance is approximately 3,660, which is choice B.

\boxed{B_6\approx3660\quad\text{(B)}}

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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 (3593) does not satisfy the retrospective balance after exactly six 250 payments; no distinct standard one-step error is identifiable.
CChoice C (3790) does not satisfy the retrospective balance after exactly six 250 payments; no distinct standard one-step error is identifiable.
DChoice D (3856) does not satisfy the retrospective balance after exactly six 250 payments; no distinct standard one-step error is identifiable.
EChoice E (3910) does not satisfy the retrospective balance after exactly six 250 payments; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: original principal recovered from a later balance

A loan charges 6% annual effective interest. After five end-of-year payments of 600, its balance immediately after payment 5 is 4,200. Calculate the original loan principal.

A
5,665.90
B
5,949.20
C
6,232.49
D
6,515.79
E
6,799.08

Variant answer in brief

At year 5, accumulated principal equals the 4,200 remaining balance plus the accumulated value of five payments. Discounting that total gives original principal 5,665.90, choice A.

Setup

Write the retrospective balance at time 5 with the original principal as the unknown.

4200=L(1.06)^5-600s_{\overline5|0.06}

Model

Move the accumulated payments to the balance side and discount five years.

L=\frac{4200+600s_{\overline5|0.06}}{(1.06)^5}

Compute

The resulting original principal is 5665.90.

L=5665.902597

Answer

The original loan was 5,665.90, which is choice A.

\boxed{L\approx5665.90\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 5 · N · 6 · I/Y · 600 · +/- · PMT · 4200 · +/- · FV · CPT · PVPV = 5665.90The payment and ending balance have the same sign, opposite the initial loan.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #232 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Loan Balances and Amortization question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: original principal recovered from a later balance

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