Verified solution · Exam FM

SOA Exam FM Sample Question #12 Solution

This Exam FM sample reference tests Comparison of Repayment Methods. The level-payment method pays 2,990 in total, so its interest is 990. Setting 11,000i = 990 gives i = 9.00%. The result agrees with the published answer key, choice B.

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 Comparison of Repayment Methods question

Setup

For the level-payment option, first determine the annual payment from the 2,000 loan value and the ten-year annuity factor at 8.07%. For the equal-principal option, the outstanding balances before interest are 2,000, 1,800, …, 200.

2000=Pa_{\overline{10}|\,0.0807}\Longrightarrow P=299

Model

Total payments under the two methods are equal. The second method’s total interest is therefore i times the sum of those ten opening balances, which is 11,000.

\text{total interest under option ii}=i(2000+1800+\cdots+200)

Compute

The level-payment method pays 2,990 in total, so its interest is 990. Setting 11,000i = 990 gives i = 9.00%.

2990-2000=11000i\Longrightarrow i=0.09

Answer

The calculation gives 9.00% for comparison of repayment methods, matching published choice B.

\boxed{i=9.00\%\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 10 N; 8.07 I/Y; 2000 +/- PV; 0 FV; CPT PMT299.00This reproduces the level-payment option before comparing total interest.

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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 (8.75%) does not match the checked comparison of repayment methods result (9.00%); no distinct standard one-step error is identifiable.
CChoice C (9.25%) does not match the checked comparison of repayment methods result (9.00%); no distinct standard one-step error is identifiable.
DChoice D (9.50%) does not match the checked comparison of repayment methods result (9.00%); no distinct standard one-step error is identifiable.
EChoice E (9.75%) does not match the checked comparison of repayment methods result (9.00%); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: five-year repayment comparison

A 1,000 five-year loan has level annual payments at 6%. A second option repays 200 principal yearly plus interest on the opening balance. Find the second option's rate that makes total payments equal.

A
5.50%
B
6.00%
C
6.23%
D
6.50%
E
7.00%

Variant answer in brief

Equating totals gives i = 0.062327, or 6.23%. This selects choice C.

Setup

Compute total payments under the five-payment level loan at 6%.

T_1=5\frac{1000}{a_{\overline5|\,0.06}}

Model

For equal-principal repayment, total interest equals i times the opening balances 1,000, 800, 600, 400, and 200.

T_2=1000+i(1000+800+600+400+200)

Compute

Equating totals gives i = 0.062327, or 6.23%.

i=\frac{T_1-1000}{3000}=0.062327

Answer

The requested value is 6.23%, so the correct choice is C.

\boxed{i=6.23\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 5 N; 6 I/Y; 1000 +/- PV; 0 FV; CPT PMT237.40Use five times this payment in the repayment comparison.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #12 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Comparison of Repayment Methods 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: five-year repayment comparison

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