Verified solution · Exam FM

SOA Exam FM Sample Question #427 Solution

This Exam FM sample reference tests Bond Realized Yield. Reinvesting all coupons at 5.7% produces an 18-year horizon value of 20117.50. Discounting it at the realized 5.18% return gives price 8105.45; that price implies bond yield 4.914%, 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 Bond Realized Yield question

Setup

The annual coupon is 420. Accumulate every coupon to the 18-year horizon at the stated reinvestment rate.

C=7{,}000(0.06)=420

H=420s_{\overline{18}|0.057}+7{,}500

Model

The realized annual return connects purchase price P to this horizon value. The bond yield i separately prices contractual cash flows at purchase.

P(1.0518)^{18}=H

P=420a_{\overline{18}|i}+7{,}500(1+i)^{-18}

Compute

The horizon value is 20117.50 and P is 8105.45. Solving the bond equation gives i = 0.0491405.

H=20{,}117.502

P=8{,}105.449

i=4.91405\%

Answer

The original bond yield is approximately 4.91%, choice D.

\boxed{i\approx4.91\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

18 · N; 8105.449 · +/− · PV; 420 · PMT; 7500 · FV; CPT · I/Y4.91405Use annual periods because coupons are annual.

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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 is below the yield that prices 420 annual coupons plus 7500 redemption to the recovered purchase price.
BChoice B is a nearby root produced by rounding the 18-year horizon value before solving for bond yield.
CChoice C discounts the redemption but does not fully include the coupon annuity at the purchase-date yield.
EChoice E substitutes the realized horizon return for the contractual yield; reinvestment at 5.7% prevents those rates from being identical.

Original practice · fully worked

Original variant: realized return from reinvested coupons

An investor pays 980 for a five-year bond that pays annual coupons of 50 and redeems for 1,050 with the fifth coupon. Each coupon is reinvested at 4% until maturity. What annual effective return is realized over the five-year holding period?

A
4.00%
B
5.10%
C
5.61%
D
6.15%
E
7.14%

Variant answer in brief

The maturity-date value of coupons and redemption is 1320.816. Equating this to 980 accumulated for five years gives a realized return of 6.1508%, choice D.

Setup

Accumulate the five coupons to the date of the final redemption.

H=50s_{\overline{5}|0.04}+1{,}050

Model

Let y be the annual effective holding-period return on the original 980 investment.

980(1+y)^5=H

Compute

The reinvested horizon value is 1320.816. Take the fifth root of the accumulation ratio.

y=\left(\frac{1{,}320.816}{980}\right)^{1/5}-1

y=0.06150797

Answer

The realized return is 6.15%, choice D.

\boxed{y\approx6.15\%\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #427 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Realized 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: realized return from reinvested coupons

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution