Verified solution · Exam FM

SOA Exam FM Sample Question #97 Solution

This Exam FM sample reference tests Bond Term from Book Values. The prospective equation gives seventeen periods after time 3, so the original term is n = 20. The result agrees with the published answer key, choice E.

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 Term from Book Values question

Setup

Use the book-value recurrence to recover the coupon: next book value equals current book value accumulated at yield minus the coupon.

1254.87(1.06)-C=1277.38\Longrightarrow C=52.7822

Model

The recurrence gives C = 52.7822. Value the remaining coupons and redemption prospectively at time 3 and solve for the remaining term.

1254.87=52.7822a_{\overline{n-3}|\,0.06}+1890v^{n-3}

Compute

The prospective equation gives seventeen periods after time 3, so the original term is n = 20.

n-3=17,\quad n=20

Answer

The calculation gives 20 for bond term from book values, matching published choice E.

\boxed{n=20\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 1254.87 +/- PV; 6 I/Y; 52.7822 PMT; 1890 FV; CPT N17.00Add the three elapsed periods to recover the original term.

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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 (16) does not match the checked bond term from book values result (20); no distinct standard one-step error is identifiable.
BChoice B (17) does not match the checked bond term from book values result (20); no distinct standard one-step error is identifiable.
CChoice C (18) does not match the checked bond term from book values result (20); no distinct standard one-step error is identifiable.
DChoice D (19) does not match the checked bond term from book values result (20); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: bond term recovered from consecutive book values

A bond yields 5% annually, pays level annual coupons, and redeems 1,000. Its book values immediately after coupons 2 and 3 are 935.37 and 942.14. Calculate the original number of annual coupon periods.

A
8
B
9
C
10
D
11
E
12

Variant answer in brief

The recurrence gives coupon 40 and the prospective equation gives eight remaining periods; adding the two elapsed periods gives ten. The original bond term is 10 years, which is choice C.

Setup

Use the one-period book-value recurrence to recover the annual coupon from the two consecutive values.

C=935.37(1.05)-942.14\approx40

Model

At time 2, value the remaining coupons and redemption prospectively and solve for the number m still outstanding.

935.37=40a_{\overline m|0.05}+1000(1.05)^{-m}

Compute

The recurrence gives coupon 40 and the prospective equation gives eight remaining periods; adding the two elapsed periods gives ten.

m=8,\quad n=m+2=10

Answer

The original bond term is 10 years, which is choice C.

\boxed{n=10\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 5 I/Y; 935.37 +/- PV; 40 PMT; 1000 FV; CPT N8.00Add the two elapsed coupon periods.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #97 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Term from Book Values 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: bond term recovered from consecutive book values

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