Verified solution · Exam FM

SOA Exam FM Sample Question #48 Solution

This Exam FM sample reference tests Principal Portions and Total Interest. The payment is 842.39, first principal is 581.14, and the loan is 5,500. Total interest is 8(842.39) − 5,500 = 1,239.12. 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 Portions and Total Interest question

Setup

In a level-payment loan, principal portions form a geometric progression with ratio 1 + i. Use the principal amount with four periods remaining to recover the payment.

699.68=Pv^4\Longrightarrow P=842.39

Model

The same progression gives the first principal portion. Since payment minus first principal equals first-period interest, dividing by i recovers the original loan amount.

P_1=Pv^8=581.14,\quad L=(P-P_1)/0.0475=5500

Compute

The payment is 842.39, first principal is 581.14, and the loan is 5,500. Total interest is 8(842.39) − 5,500 = 1,239.12.

I_{\text{total}}=8P-L=1239.12

Answer

The calculation gives 1239 for principal portions and total interest, matching published choice A.

\boxed{I=1239\quad\text{(A)}}

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All 461 Exam FM sample solutions in syllabus order

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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 (1647) does not match the checked principal portions and total interest result (1239); no distinct standard one-step error is identifiable.
CChoice C (1820) does not match the checked principal portions and total interest result (1239); no distinct standard one-step error is identifiable.
DChoice D (2319) does not match the checked principal portions and total interest result (1239); no distinct standard one-step error is identifiable.
EChoice E (2924) does not match the checked principal portions and total interest result (1239); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: total interest from a complete six-payment schedule

A 4,000 loan is amortized by six equal annual payments at 5% annual effective interest. Calculate the total interest paid over the life of the loan.

A
650.00
B
700.00
C
728.42
D
760.00
E
800.00

Variant answer in brief

The annual payment is 788.07, and six payments exceed principal by 728.42. Total interest is 728.42, so choice C is correct.

Setup

Find the annual payment that amortizes 4,000 over six years at 5%.

R=4000/a_{\overline6|0.05}=788.069872

Model

Because the six payments retire all principal, total interest is total payments minus the original loan.

I_{total}=6R-4000

Compute

The annual payment is 788.07, and six payments exceed principal by 728.42.

I_{total}=728.419235

Answer

Total interest is 728.42, so choice C is correct.

\boxed{I_{total}=728.42\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 6 N; 5 I/Y; 4000 +/- PV; 0 FV; CPT PMT788.07Multiply the payment by six and subtract 4,000.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #48 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Principal Portions and Total Interest question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: total interest from a complete six-payment schedule

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