Verified solution · Exam FM

SOA Exam FM Sample Question #98 Solution

This Exam FM sample reference tests Bond Term from Discount Accrual. There are ten periods after period 3, so maturity is at period 13, equal to 6.5 years. 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 Term from Discount Accrual question

Setup

Use the quoted discount accrual to recover the book value immediately before the next coupon. At 4%, interest minus coupon equals the 8.44 increase in book value.

B_3(1.04)-87.50=B_3+8.44\Longrightarrow B_3=2398.5

Model

This gives B₃ = 2,398.5. Equate that book value to the present value of the remaining 87.50 coupons and 2,500 redemption to solve the remaining half-year periods.

2398.5=87.5a_{\overline{m-3}|\,0.04}+2500v^{m-3}

Compute

There are ten periods after period 3, so maturity is at period 13, equal to 6.5 years.

m-3=10,\quad m=13,\quad n=m/2=6.5

Answer

The calculation gives 6.5 for bond term from discount accrual, matching published choice A.

\boxed{n=6.5\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 2398.5 +/- PV; 4 I/Y; 87.5 PMT; 2500 FV; CPT N10.00Ten periods remain after period 3; divide the total thirteen half-years by two.

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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 (7.0) does not match the checked bond term from discount accrual result (6.5); no distinct standard one-step error is identifiable.
CChoice C (9.5) does not match the checked bond term from discount accrual result (6.5); no distinct standard one-step error is identifiable.
DChoice D (12.0) does not match the checked bond term from discount accrual result (6.5); no distinct standard one-step error is identifiable.
EChoice E (14.0) does not match the checked bond term from discount accrual result (6.5); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: maturity from a semiannual discount-accrual observation

A semiannual-pay discount bond yields 4% per half-year, pays coupons of 60, and redeems 2,000. Immediately after coupon 4, the discount amortized during the next half-year is 14.61. Calculate the original term in years.

A
5.0 years
B
5.5 years
C
6.0 years
D
6.5 years
E
7.0 years

Variant answer in brief

The prospective equation gives eight remaining half-years; with four elapsed, the total is twelve half-years or 6.0 years. The original term is 6.0 years, selecting choice C.

Setup

Discount amortization equals yield interest on opening book value minus the coupon, so recover the book value after coupon 4.

14.61=0.04B_4-60\Longrightarrow B_4\approx1865.35

Model

Set that book value equal to the prospective value of remaining coupons and redemption to obtain the remaining half-year count.

B_4=60a_{\overline m|0.04}+2000(1.04)^{-m}

Compute

The prospective equation gives eight remaining half-years; with four elapsed, the total is twelve half-years or 6.0 years.

m=8,\quad n=(4+8)/2=6

Answer

The original term is 6.0 years, selecting choice C.

\boxed{n=6.0\text{ years}\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 4 I/Y; 1865.35 +/- PV; 60 PMT; 2000 FV; CPT N8.00Add four elapsed half-years and divide the total by two.

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ActuaryProof. “SOA Exam FM Sample Question #98 — 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 Discount Accrual 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: maturity from a semiannual discount-accrual observation

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