Verified solution · Exam FM

SOA Exam FM Sample Question #59 Solution

This Exam FM sample reference tests Coupon-Spread Bond Pricing. The factor 13.3528 gives j = 4.2% per half-year. The nominal annual yield convertible semiannually is 2j = 8.4%. The result agrees with the published answer key, 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 Coupon-Spread Bond Pricing question

Setup

Subtract the two bond-price equations. Because redemption cash flows are identical, they cancel and only the 400 coupon difference remains.

P_A-P_B=400a_{\overline{20}|\,j}=5341.12

Model

The price difference therefore equals 400 times a twenty-period annuity factor at the half-year yield j. Solve the factor equation before converting the quote.

a_{\overline{20}|\,j}=13.3528

Compute

The factor 13.3528 gives j = 4.2% per half-year. The nominal annual yield convertible semiannually is 2j = 8.4%.

j=0.042,\quad i^{(2)}=2j=0.084

Answer

The calculation gives 0.084 for coupon-spread bond pricing, matching published choice D.

\boxed{i^{(2)}=8.4\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 20 N; 5341.12 +/- PV; 400 PMT; 0 FV; CPT I/Y; × 2 =8.40The redemption amounts cancel, so the price spread is a level annuity.

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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 (0.042) does not match the checked coupon-spread bond pricing result (0.084); no distinct standard one-step error is identifiable.
BChoice B (0.043) does not match the checked coupon-spread bond pricing result (0.084); no distinct standard one-step error is identifiable.
CChoice C (0.081) does not match the checked coupon-spread bond pricing result (0.084); no distinct standard one-step error is identifiable.
EChoice E (0.086) does not match the checked coupon-spread bond pricing result (0.084); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: yield inferred from a ten-year coupon-price spread

Two ten-year annual-pay bonds have the same redemption amount and yield. Their annual coupons differ by 20, and their prices differ by 154.43. Calculate the common annual effective yield.

A
3.0%
B
4.0%
C
5.0%
D
6.0%
E
7.0%

Variant answer in brief

Dividing by 20 gives an annuity factor of 7.721735, whose ten-period yield is 5.0%. The common annual effective yield is 5.0%, selecting choice C.

Setup

Subtract the two prices so the identical redemption present values cancel.

P_1-P_2=154.43=20a_{\overline{10}|i}

Model

The remaining price spread is the present value of a ten-payment coupon difference of 20.

a_{\overline{10}|i}=7.721735

Compute

Dividing by 20 gives an annuity factor of 7.721735, whose ten-period yield is 5.0%.

a_{\overline{10}|i}=7.721735\Longrightarrow i=0.05

Answer

The common annual effective yield is 5.0%, selecting choice C.

\boxed{i=5.0\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 10 N; 154.43 +/- PV; 20 PMT; 0 FV; CPT I/Y5.00Redemption cancels before the TVM entry.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #59 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Coupon-Spread Bond Pricing 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: yield inferred from a ten-year coupon-price spread

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