Verified solution · Exam FM

SOA Exam FM Sample Question #407 Solution

This Exam FM sample reference tests Loan Amortization. Interest-only payments leave principal 150,000 after 60 months; at the later 0.5% monthly rate, payments of 1,000 require 278 more months, for 338 total payments, choice E.

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.

Read the solution Open official source

Independent solution

How to solve this Loan Amortization question

Setup

The first five years' payments cover interest only, so they do not reduce principal.

B_{60}=150000

Model

At month 60, value the later level-payment stream using the new 0.5% monthly rate.

150000=1000a_{\overline{n}|\,0.06/12}

Compute

The amortizing phase requires approximately 278 payments.

n\approx278

Answer

Including the initial 60 interest-only payments gives 338 total, corresponding to choice E.

\boxed{60+278=338\text{ payments}\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 0.5 I/Y; 150000 PV; 1000 +/- PMT; 0 FV; CPT NN ≈ 278Add the 60 interest-only payments to obtain 338 total.

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

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 unchanged balance after interest-only payments and later annuity term; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the unchanged balance after interest-only payments and later annuity term; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the unchanged balance after interest-only payments and later annuity term; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the unchanged balance after interest-only payments and later annuity term; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: payment after an interest-only phase

A borrower pays interest only on 150,000 for five years. The balance is then amortized over 240 months at 6% nominal convertible monthly. Determine the required month-end payment during the amortizing phase.

A
974.65
B
1,024.65
C
1,074.65
D
1,124.65
E
1,174.65

Variant answer in brief

The interest-only phase leaves balance 150,000; dividing by the 240-month annuity factor gives payment 1,074.65, choice C.

Setup

Interest-only payments preserve the full principal through month 60.

150000=Pa_{\overline{240}|\,0.06/12}

Model

The later payments form a 240-month annuity-immediate at 0.5% monthly.

P=\frac{150000}{a_{\overline{240}|\,0.005}}

Compute

Dividing principal by that factor gives 1,074.6466.

P=1074.6466

Answer

The amortizing payment is 1,074.65, corresponding to choice C.

\boxed{P=1074.65\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 240 N; 0.5 I/Y; 150000 PV; 0 FV; CPT PMTPMT = -1074.65

Keep practicing

Turn this solution into a complete study sequence

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.

See the Exam FM study manual PDF — $49 More Exam FM Loans practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #407 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Loan 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: payment after an interest-only phase

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