Verified solution · Exam FM

SOA Exam FM Sample Question #356 Solution

This Exam FM sample reference tests Linking a Force of Interest to Nominal Discount. The force simplifies to 1/(10+t), so 1000 grows from time 2 to 6 by 16/12, giving X = 1333.33. Discounting this back eight quarters at 2% discount per quarter gives Y = 1134.35, choice C.

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 Linking a Force of Interest to Nominal Discount question

Setup

Simplify the stated force and integrate over the investment interval.

\delta_t=\frac{1}{10+t}

X=1{,}000\exp\left(\int_2^6\frac{dt}{10+t}\right)

Model

The continuous-force accumulation is a ratio of endpoints.

X=1{,}000\frac{16}{12}=1{,}333.3333

Compute

A nominal discount rate of 8% convertible quarterly has quarterly discount 2%.

X=Y(1-0.02)^{-8}

Y=X(0.98)^8=1{,}134.3507

Answer

The required initial amount is approximately 1134, choice C.

\boxed{Y\approx1{,}134\quad\text{(C)}}

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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 treats the nominal discount rate as a nominal interest rate when moving Y forward.
BChoice B uses only seven quarterly periods over the two-year interval.
DChoice D integrates the force from time zero rather than from the investment's time-2 deposit date.
EChoice E replaces the time-varying force by its value at time 2 for all four years.

Original practice · fully worked

Original variant: nominal discount rate from two accumulation paths

A 1,000 deposit grows from time 0 to time 4 under force of interest 1/(4+t). A separate 1,500 deposit must reach the same terminal amount in two years under a nominal annual discount rate d convertible semiannually. Determine d.

A
10.84%
B
12.50%
C
13.88%
D
15.25%
E
16.67%

Variant answer in brief

The force path doubles 1000 to 2000. Solving 1500 accumulated through four semiannual discount periods to 2000 gives d = 13.8790%, choice C.

Setup

Integrate the force to find the common terminal target.

F=1{,}000\exp\left(\int_0^4\frac{dt}{4+t}\right)=2{,}000

Model

A semiannual nominal discount rate uses discount d divided by two each half-year.

1{,}500\left(1-\frac d2\right)^{-4}=2{,}000

Compute

Solve the fourth-power equation.

d=2\left[1-\left(\frac{1{,}500}{2{,}000}\right)^{1/4}\right]=0.1387903

Answer

The nominal discount rate is 13.88%, choice C.

\boxed{d\approx13.88\%\quad\text{(C)}}

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ActuaryProof. “SOA Exam FM Sample Question #356 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Linking a Force of Interest to Nominal Discount question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: nominal discount rate from two accumulation paths

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution