Verified solution · Exam FM

SOA Exam FM Sample Question #345 Solution

This Exam FM sample reference tests Bond Term from Price and Yield. The 49 semiannual coupon on face 980 implies a 10% nominal coupon rate. The half-year yield is therefore 5.9%, and the price equation is satisfied by twelve half-years, or six years, 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 Price and Yield question

Setup

Infer the nominal annual coupon rate from the semiannual coupon amount.

49=980\frac r2

r=0.10

Model

Add 1.8 percentage points to obtain the nominal yield and divide by two.

j^{(2)}=0.118

q=0.059

Compute

Solve the bond price equation for the number of half-year periods.

915.70=49a_{\overline{2n}|0.059}+1{,}000(1.059)^{-2n}

2n=12

Answer

The maturity is six years, choice E.

\boxed{n=6\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

5.9 · I/Y; 915.70 · +/− · PV; 49 · PMT; 1000 · FV; CPT · N12.00The display is the number of half-year periods, so divide 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.

AChoice A stops at four half-year periods and reads that count directly as years.
BChoice B solves twelve half-year periods correctly but divides the period count by four.
CChoice C uses the 10% coupon rate as the yield and obtains a shorter term.
DChoice D subtracts rather than adds the 1.8-point yield spread from the coupon rate.

Original practice · fully worked

Original variant: redemption amount from a quoted price

An eight-year bond pays 40 every six months and is priced at 950. The nominal annual yield is 6% convertible semiannually. Determine the redemption amount paid with the final coupon.

A
650.00
B
684.42
C
718.20
D
750.00
E
802.35

Variant answer in brief

After valuing the sixteen coupons at 3% per half-year, the remaining price supports a redemption amount of 718.20, choice C.

Setup

Use sixteen half-year periods and a 3% periodic yield.

n=16,\qquad q=0.06/2=0.03

Model

Let F be the redemption amount and write the price equation.

950=40a_{\overline{16}|0.03}+F(1.03)^{-16}

Compute

Solve the linear equation in F.

F=718.1959

Answer

The redemption amount is 718.20, choice C.

\boxed{F=718.20\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

16 · N; 3 · I/Y; 950 · +/− · PV; 40 · PMT; CPT · FV718.20Cash-flow signs place price opposite the coupons and redemption.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #345 — 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 Price and Yield 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: redemption amount from a quoted price

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