Verified solution · Exam FM

SOA Exam FM Sample Question #401 Solution

This Exam FM sample reference tests Loan Amortization. Interest in the final payment equals payment times i divided by one plus i, so the level payment is 1,000; first-year interest is 955.50 and first principal is 44.50, 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.

Read the solution Open official source

Independent solution

How to solve this Loan Amortization question

Setup

Immediately before the final payment, the balance is one payment discounted one year.

65.42=P\frac{0.07}{1.07}\Longrightarrow P=1000

Model

Therefore final-payment interest identifies the level payment directly.

I_1=13650(0.07)=955.50

Compute

The first payment's interest is 7% of the original advance; the remainder is principal.

PR_1=P-I_1=1000-955.50=44.50

Answer

Principal repaid in the first payment is 44.50, corresponding to choice A.

\boxed{PR_1=44.50\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 7 I/Y; 13650 PV; 1000 +/- PMT; 0 FV; CPT N; 2nd AMORT; P1=1; P2=1PRN = 44.50The payment 1,000 is first recovered from the final-payment interest identity.

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.

BChoice B is inconsistent with the last-payment interest relation and first-payment split; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the last-payment interest relation and first-payment split; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the last-payment interest relation and first-payment split; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the last-payment interest relation and first-payment split; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: last-payment interest from the first principal portion

A loan earns 6% effective annually and is repaid by exactly 20 equal year-end payments. The principal repaid by the first payment is 100. Determine the interest included in the twentieth and final payment.

A
13.15
B
15.15
C
18.15
D
21.15
E
24.15

Variant answer in brief

Successive principal portions grow by 6%, so the final principal is 100 times 1.06 to the nineteenth power and its interest is 18.15, choice C.

Setup

For a level-payment loan, each principal portion is the preceding portion accumulated for one year.

PR_{t+1}=1.06PR_t

Model

Grow the first principal portion through nineteen successive periods to obtain the twentieth principal portion.

PR_{20}=100(1.06)^{19}=302.5599

Compute

Immediately before the last payment, that final principal portion is the outstanding balance, so its 6% interest is 18.1536.

I_{20}=0.06PR_{20}=18.1536

Answer

The final payment contains 18.15 of interest, corresponding to choice C.

\boxed{I_{20}=18.15\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 20 N; 6 I/Y; 320.7135 +/- PMT; 0 FV; CPT PV; 2nd AMORT; P1=20; P2=20INT = -18.15; PRN = -302.56The implied payment is 100 times 1.06 to the twentieth power.

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 #401 — 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: last-payment interest from the first principal portion

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