Verified solution · Exam FM

SOA Exam FM Sample Question #137 Solution

This Exam FM sample reference tests Bond Valuation. At year 20 the reinvested first bond is worth 13.4106 million and the sale of the second is worth 15.5184 million; subtracting the six-million outlay gives a 22.929-million gain, 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 Valuation question

Setup

Track both zero-coupon positions to the common year-20 measurement date.

V_{10\to20}=2(1.08)^{10}(1.12)^{10}=13.4106

Model

The first matures at year ten and is reinvested for another decade; the second's year-30 redemption is discounted back ten years at the buyer's yield.

R_{30}=4(1.08)^{30}=40.2506

Compute

Those year-20 proceeds total 28.929 million.

P_{20}=40.2506(1.10)^{-10}=15.5184

Answer

After subtracting the original six-million investment, the gain is about 23 million, choice A.

\boxed{X=13.4106+15.5184-6=22.929\text{ million}\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 8 I/Y; 2 +/- PV; 0 PMT; CPT FVFV = 4.31785END mode; I/Y is annual and the first holding grows for ten years.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 12 I/Y; 4.31785 +/- PV; 0 PMT; CPT FVFV = 13.4106END mode; I/Y is the annual reinvestment rate for the following ten years.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 30 N; 8 I/Y; 4 +/- PV; 0 PMT; CPT FVFV = 40.2506END mode; I/Y is annual and gives the second zero's maturity value.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 10 I/Y; 0 PMT; 40.2506 FV; CPT PVPV = -15.5184END mode; I/Y is the annual sale yield for the ten years remaining at sale.

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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 is inconsistent with the common year-20 value of both zero-coupon strategies; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the common year-20 value of both zero-coupon strategies; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the common year-20 value of both zero-coupon strategies; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the common year-20 value of both zero-coupon strategies; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: proceeds from a library's staggered zero-coupon reserve

A library invests 1 million in an eight-year zero and 2 million in a twenty-year zero, each initially yielding 6%. At year 8 the first maturity is reinvested for two years at 4%. At year 10 the other zero is sold to yield 8% for its remaining ten years. Find the gain over the original 3 million, in millions.

A
1.20
B
1.45
C
1.695
D
1.90
E
2.10

Variant answer in brief

The year-10 proceeds total 4.69495 million, so the gain is 1.69495 million, choice C.

Setup

Move both investments to year ten, the date when proceeds are compared.

V_1=1(1.06)^8(1.04)^2=1.723906

Model

The first position grows through its original term and two-year reinvestment; the second position is the present value at year ten of its year-20 maturity.

V_2=2(1.06)^{20}(1.08)^{-10}=2.971049

Compute

Their values are 1.723906 and 2.971049 million, totaling 4.694955 million.

G=V_1+V_2-3=1.694955

Answer

Subtracting the original three million gives a gain of 1.695 million, choice C.

\boxed{G=1.695\text{ million}\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 8 N; 6 I/Y; 1 +/- PV; 0 PMT; CPT FVFV = 1.593848END mode; I/Y is annual and grows the first zero to its year-8 maturity.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 2 N; 4 I/Y; 1.593848 +/- PV; 0 PMT; CPT FVFV = 1.723906END mode; I/Y is the annual reinvestment rate for years 8 through 10.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 20 N; 6 I/Y; 2 +/- PV; 0 PMT; CPT FVFV = 6.414271END mode; I/Y is annual and gives the second zero's year-20 maturity value.
2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 8 I/Y; 0 PMT; 6.414271 FV; CPT PVPV = -2.971049END mode; I/Y is the annual sale yield for the ten years remaining at year 10.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #137 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Bond Valuation 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: proceeds from a library's staggered zero-coupon reserve

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