Verified solution · Exam FM

SOA Exam FM Sample Question #317 Solution

This Exam FM sample reference tests Bond Pricing and Yields. Per unit face, the combined price equals two discounted redemptions plus coupon rates rA and rA + 0.005 times the 30-year annuity factor. Solving the total price ratio 3 gives rA = 10.78%, 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.

Read the solution Open official source

Independent solution

How to solve this Bond Pricing and Yields question

Setup

Write the two 30-year prices per 1,000 face at the common 7% yield.

P_A=1000[r_Aa_{\overline{30}|0.07}+v^{30}]

P_B=1000[(r_A+0.005)a_{\overline{30}|0.07}+v^{30}]

Model

Divide the total price by 1,000 and combine like terms.

3=2v^{30}+(2r_A+0.005)a_{\overline{30}|0.07}

Compute

Solving gives Bond A coupon rate 10.779320%.

r_A=0.1077932018

Answer

Bond A's annual coupon rate is approximately 10.78%, selecting choice B.

\boxed{r_A\approx10.78\%\quad\text{(B)}}

Continue without hunting through PDFs

All 461 Exam FM sample solutions in syllabus order

The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.

See inside the Exam FM study manual PDF

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 (10.06%) does not satisfy the combined price of both 30-year coupon and redemption streams at 7%; no distinct standard one-step error is identifiable.
CChoice C (10.90%) does not satisfy the combined price of both 30-year coupon and redemption streams at 7%; no distinct standard one-step error is identifiable.
DChoice D (11.31%) does not satisfy the combined price of both 30-year coupon and redemption streams at 7%; no distinct standard one-step error is identifiable.
EChoice E (11.84%) does not satisfy the combined price of both 30-year coupon and redemption streams at 7%; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: coupon-rate spread recovered from a two-bond total price

Two 30-year 1,000-face bonds both yield 7% annually. Bond A's coupon rate is 6%; Bond B's coupon rate is 6% plus an unknown spread s. Their combined price is 1875.91. Calculate s.

A
0.80%
B
0.85%
C
0.90%
D
0.95%
E
1.00%

Variant answer in brief

Subtracting the two known 6% coupon streams and both redemptions from the quoted total leaves s times the 30-year annuity factor. The spread is 1.00%, choice E.

Setup

Write the combined price at the common 7% yield.

P=1000[(0.06a_{30}+v^{30})+((0.06+s)a_{30}+v^{30})]

Model

Remove both known redemption values and the two 6% coupon components.

1000s a_{\overline{30}|0.07}=P-2000v^{30}-120a_{\overline{30}|0.07}

Compute

Solving gives spread 1.000000%.

s=0.0100000000

Answer

The coupon-rate spread is 1.00%, selecting choice E.

\boxed{s=1.00\%\quad\text{(E)}}

Keep practicing

Turn this solution into a complete study sequence

The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.

See the Exam FM study manual PDF — $49 More Exam FM Bonds practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #317 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Pricing and Yields question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: coupon-rate spread recovered from a two-bond total price

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution