Verified solution · Exam FM

SOA Exam FM Sample Question #255 Solution

This Exam FM sample reference tests Loan Balances and Amortization. A 20-year lump sum produces interest 1.65330X. Ten level payments produce total interest 0.29505X. Their difference equals 1,000, giving X = 736.24 and choice D.

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

Express total interest under the 20-year lump-sum repayment.

I_L=X[(1.05)^{20}-1]

Model

For ten level payments, total interest is total payments minus principal.

I_A=10\frac{X}{a_{\overline{10}|0.05}}-X

Compute

Set the lump-sum interest 1,000 above the level-payment interest and solve X = 736.2404.

I_L-I_A=1000

X=736.24042723

Answer

The borrowed amount is approximately 736, selecting choice D.

\boxed{X\approx736\quad\text{(D)}}

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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 (389) does not satisfy the 1,000 difference between total interest under the two repayment schedules; no distinct standard one-step error is identifiable.
BChoice B (540) does not satisfy the 1,000 difference between total interest under the two repayment schedules; no distinct standard one-step error is identifiable.
CChoice C (704) does not satisfy the 1,000 difference between total interest under the two repayment schedules; no distinct standard one-step error is identifiable.
EChoice E (954) does not satisfy the 1,000 difference between total interest under the two repayment schedules; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: extra interest from deferring repayment to one maturity date

A 2,000 loan charges 6% annually. Compare repayment by one lump sum at year 15 with repayment by eight level annual payments beginning at year 1. Calculate how much more total interest the lump-sum method produces.

A
1,884.06
B
1,994.89
C
2,105.71
D
2,216.54
E
2,327.37

Variant answer in brief

The lump-sum interest is 2,793.12, while eight level payments produce 576.58 of interest. The difference is 2,216.54, choice D.

Setup

Compute maturity interest under the single-payment method.

I_L=2000[(1.06)^{15}-1]

Model

Compute the eight-year level payment and subtract principal from total payments.

R=\frac{2000}{a_{\overline8|0.06}}

I_A=8R-2000

Compute

The two interest totals are 2793.12 and 576.58, differing by 2216.54.

I_L-I_A=2216.54130383

Answer

Deferring repayment creates 2,216.54 more interest, selecting choice D.

\boxed{I_L-I_A\approx2216.54\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #255 — 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

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: extra interest from deferring repayment to one maturity date

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution