Verified solution · Exam FM

SOA Exam FM Sample Question #330 Solution

This Exam FM sample reference tests Interest Credited over a Specified Year. Under force 1/(t+1), the first account grows from 9 at time 2 to 12 at time 3, earning 3 during the third year. The corresponding bank-account interest factor is 0.055125, giving X = 54.42 and 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 Interest Credited over a Specified Year question

Setup

Integrating the force gives an accumulation proportional to t plus 1. The initial deposit of 3 therefore has value 3(t+1).

A(t)=3\exp\left(\int_0^t\frac{ds}{s+1}\right)=3(t+1)

Model

Interest earned during the third year is the value increase from time 2 to time 3.

A(3)-A(2)=12-9=3

Compute

The bank account's third-year interest is the difference of its time-3 and time-2 values.

X(1.05^3-1.05^2)=0.055125X

X=\frac3{0.055125}=54.4218

Answer

The required bank deposit is 54.4, choice E.

\boxed{X\approx54.4\quad\text{(E)}}

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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 equates 3 to one year of 5% interest on X, ignoring that the third-year base has already grown for two years.
BChoice B uses the first account's time-3 balance 12 rather than its third-year interest of 3.
CChoice C compares total three-year interest in the two accounts instead of interest earned only in year 3.
DChoice D uses the bank's second-year interest increment rather than the third-year increment.

Original practice · fully worked

Original variant: match second-year interest under two models

A deposit of 5 is placed in a fund with force of interest 2 divided by t plus 2. Another deposit X earns 4% effective annually. Find X so that the interest earned during the second year, from time 1 to time 2, is the same in both accounts.

A
168.27
B
192.31
C
200.00
D
210.34
E
218.75

Variant answer in brief

The force-based account earns 8.75 during year 2. Dividing by 1.04 squared minus 1.04 gives X = 210.34, choice D.

Setup

Integrating 2/(t+2) makes the first balance proportional to (t+2) squared.

A(t)=5\left(\frac{t+2}{2}\right)^2

Model

Compute its increase from time 1 to time 2.

A(2)-A(1)=5\left(2^2-1.5^2\right)=8.75

Compute

Set this equal to second-year interest in the 4% account.

X(1.04^2-1.04)=8.75

X=210.3365

Answer

The matching deposit is 210.34, choice D.

\boxed{X=210.34\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #330 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Interest Credited over a Specified Year question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: match second-year interest under two models

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution