Verified solution · Exam FM

SOA Exam FM Sample Question #267 Solution

This Exam FM sample reference tests Loan Balances and Amortization. After payment 180, the raised payment 2,000 amortizes the balance over 120 months, giving balance 180146.91. That balance implies original payment 1520.18 for the remaining 180 months, and the 360-month loan value is 253553.61, 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 Loan Balances and Amortization question

Setup

Paying off five years early leaves 120 payments after the 180th payment rather than 180.

B_{180}=2000a_{\overline{120}|0.005}

Model

Before the change, that same balance equals the present value of 180 original payments.

B_{180}=Pa_{\overline{180}|0.005}

Compute

The balance is 180146.91, the original payment is 1520.18, and its 360-payment present value is 253553.61.

L=Pa_{\overline{360}|0.005}=253553.60533349

Answer

The original loan was approximately 253,554, selecting choice A.

\boxed{L\approx253554\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 120 · N · 0.5 · I/Y · 0 · FV · 2000 · PMT · CPT · PVPV = -180146.91
180 · N · 180146.91 · +/- · PV · 0 · FV · CPT · PMTPMT = 1520.18
360 · N · 0 · FV · CPT · PVPV = -253553.61

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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 (277,772) does not satisfy the common month-180 balance under the original and accelerated payment schedules; no distinct standard one-step error is identifiable.
CChoice C (310,414) does not satisfy the common month-180 balance under the original and accelerated payment schedules; no distinct standard one-step error is identifiable.
DChoice D (330,347) does not satisfy the common month-180 balance under the original and accelerated payment schedules; no distinct standard one-step error is identifiable.
EChoice E (333,583) does not satisfy the common month-180 balance under the original and accelerated payment schedules; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: accelerated monthly payment required after a scheduled balance date

A 200,000 mortgage is originally amortized by level monthly payments over 25 years at 5% nominal interest convertible monthly. Immediately after payment 120, the borrower wants to retire the remaining balance with 96 further level payments at the same rate. Calculate the new monthly payment.

A
1,778.17
B
1,871.76
C
1,965.34
D
2,058.93
E
2,152.52

Variant answer in brief

The original payment is 1169.18, leaving balance 147,848.95 after 120 payments. Amortizing that balance over 96 months requires payment 1,871.76, choice B.

Setup

Compute the original 300-month payment at the monthly rate 5% divided by 12.

R=\frac{200000}{a_{\overline{300}|0.05/12}}

Model

After payment 120, value the 180 remaining original payments to obtain the balance.

B_{120}=Ra_{\overline{180}|0.05/12}

Compute

The balance is 147848.95. Dividing by the 96-payment factor gives new payment 1871.76.

R_{\mathrm{new}}=\frac{B_{120}}{a_{\overline{96}|0.05/12}}=1871.75589562

Answer

The accelerated monthly payment is 1,871.76, selecting choice B.

\boxed{R_{\mathrm{new}}\approx1871.76\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 300 · N · 0.416667 · I/Y · 200000 · +/- · PV · 0 · FV · CPT · PMTPMT = 1169.18
180 · N · 0 · FV · CPT · PVPV = -147848.95
96 · N · 147848.95 · +/- · PV · CPT · PMTPMT = 1871.76

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #267 — 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

BA II Plus keystrokes

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: accelerated monthly payment required after a scheduled balance date

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