Verified solution · Exam FM

SOA Exam FM Sample Question #189 Solution

This Exam FM sample reference tests Bond Valuation. The given redemption present value fixes the term discount factor; the coupon annuity factor is 8.87037, so price is 955.81, nearest choice C.

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 Valuation question

Setup

Work in half-year periods, where the coupon is 40 and the yield per period is 5%.

601=1080v^n\Longrightarrow v^n=\frac{601}{1080}

Model

Use the stated present value of redemption to recover the terminal discount factor without solving for n.

a_{\overline{n}|\,0.05}=\frac{1-v^n}{0.05}=8.87037

Compute

That factor determines the coupon-annuity value; adding the redemption present value gives 955.81.

P=40a_{\overline{n}|\,0.05}+601=955.81

Answer

The bond purchase price rounds to 956, which is choice C.

\boxed{P\approx956\quad\text{(C)}}

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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 is inconsistent with the redemption-factor plus coupon-annuity price equation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the redemption-factor plus coupon-annuity price equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the redemption-factor plus coupon-annuity price equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the redemption-factor plus coupon-annuity price equation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: recover a bond coupon from price

A bond redeems for 1,100 and pays level annual coupons. Its annual effective yield is 6%. The present value of redemption is 550, and the total bond price is 1,050. Determine the annual coupon.

A
40
B
50
C
60
D
70
E
80

Variant answer in brief

Redemption has discount factor 0.5, making the coupon annuity factor 8.3333; the 500 coupon value therefore requires coupon 60, choice C.

Setup

Use the redemption present value to identify the discount factor through maturity.

550=1100v^n\Longrightarrow v^n=0.5

Model

Convert that factor into the present-value factor for the annual coupon annuity.

a_{\overline{n}|\,0.06}=\frac{1-0.5}{0.06}=8.333333

Compute

Coupons account for 500 of the price, so dividing by 8.333333 gives 60.

C=\frac{1050-550}{8.333333}=60

Answer

The annual coupon is 60, corresponding to choice C.

\boxed{C=60\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #189 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Valuation question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: recover a bond coupon from price

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution