Worked solution · Exam FM

SOA Exam FM Sample Question #215 Solution

This Exam FM sample reference tests Geometrically Increasing Deposits. Accumulating each of the ten geometrically increasing deposits at 4% gives a factor of 17.902263, so the first deposit is 279.29, choice D.

Independent analysis by ActuaryProof · reviewed October 6, 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 Geometrically Increasing Deposits question

Setup

Let X be the time-1 deposit. Deposit t is X times 1.092 to the power t minus 1 and then accumulates to time 10 at 4%.

C_t=X(1.092)^{t-1}

Model

Write the time-10 value as a finite geometric sum of deposit growth and investment accumulation.

5000=X\sum_{t=1}^{10}(1.092)^{t-1}(1.04)^{10-t}

Compute

The accumulated-value factor is 17.902263. Dividing the target fund by this factor gives the first deposit.

X=\frac{5000}{17.902263}=279.2943

Answer

The first deposit rounds to 279, so the correct answer is D.

\boxed{X\approx279\quad\text{(D)}}

Test the method on unseen problems

Financial Mathematics Practice Examination I

30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.

See the cover and sample pages

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 discounts the growing deposits to time 0 but does not carry that value forward to time 10.
BChoice B treats the deposits as level and ignores their 9.2% annual growth.
CChoice C applies ten growth increases to the final deposit. There are only nine increases from deposit 1 to deposit 10.
EChoice E adds the 4% fund rate and 9.2% deposit growth as one rate instead of respecting the payment dates.

Original practice · fully worked

Original variant: accumulation of a growing reserve schedule

A laboratory deposits 250 at the end of year one into a reserve. Each later annual deposit is 5% larger than the preceding deposit, for a total of 12 deposits. The reserve earns 6% annually. Determine the value immediately after the twelfth deposit.

A
4,728
B
5,126
C
5,409
D
5,782
E
6,104

Answer and calculation

Accumulating all 12 growing deposits at their individual dates gives 5,408.50, which is choice C.

Setup

Deposit t is 250 times 1.05 to the power t minus 1 and earns 6% until time 12.

C_t=250(1.05)^{t-1}

Model

Sum the time-12 value of all twelve deposits.

F_{12}=250\sum_{t=1}^{12}(1.05)^{t-1}(1.06)^{12-t}

Compute

Evaluating the finite sum gives 5,408.5036.

F_{12}=5408.5036

Answer

The reserve holds approximately 5,409, so choice C is correct.

\boxed{F_{12}\approx5409\quad\text{(C)}}

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How to solve this Geometrically Increasing Deposits question

Setup

Model

Compute

Answer

Financial Mathematics Practice Examination I

Why the other letters tempt

Original variant: accumulation of a growing reserve schedule

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM Annuities and Non-contingent Cash Flows