Verified solution · Exam FM

SOA Exam FM Sample Question #93 Solution

This Exam FM sample reference tests Bond Redemption Value. With j = 3.465%, solving the linear equation gives F = 9,918. 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 Bond Redemption Value question

Setup

Convert the annual effective yield 7.05% to the equivalent half-year yield j. There are fifty semiannual coupon periods, and each coupon is 3.5% of the unknown redemption amount F.

j=\sqrt{1.0705}-1=0.03465,\quad r=0.035,\quad n=50

Model

The observed price 10,000 equals F times the sum of the discounted redemption factor and coupon-annuity factor.

10000=F(v^n+ra_{\overline n|\,j})

Compute

With j = 3.465%, solving the linear equation gives F = 9,918.

F=9918

Answer

The calculation gives 9,918 for bond redemption value, matching published choice A.

\boxed{F=9918\quad\text{(A)}}

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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 (9,942) does not match the checked bond redemption value result (9,918); no distinct standard one-step error is identifiable.
CChoice C (9,981) does not match the checked bond redemption value result (9,918); no distinct standard one-step error is identifiable.
DChoice D (10,059) does not match the checked bond redemption value result (9,918); no distinct standard one-step error is identifiable.
EChoice E (10,083) does not match the checked bond redemption value result (9,918); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: price from a fixed coupon and redemption schedule

An eight-year bond pays annual coupons of 50 and redeems 1,000. Investors require a 6% annual effective yield. Calculate the bond price.

A
844.11
B
891.01
C
937.90
D
984.80
E
1031.69

Variant answer in brief

The two present-value components total 937.90. The bond price is 937.90, selecting choice C.

Setup

Coupon and redemption are both known; the requested quantity is price, reversing a redemption-value problem.

C=50,\quad F=1000,\quad n=8,\quad i=0.06

Model

Discount the eight coupons as an annuity and the known redemption as a lump sum.

P=50a_{\overline8|0.06}+1000(1.06)^{-8}

Compute

The two present-value components total 937.90.

P=937.902062

Answer

The bond price is 937.90, selecting choice C.

\boxed{P=937.90\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #93 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Redemption Value question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: price from a fixed coupon and redemption schedule

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution