Verified solution · Exam FM

SOA Exam FM Sample Question #83 Solution

This Exam FM sample reference tests Growing Deposits and Withdrawals. The implied yield is 8.2637%, and substitution in the thirty-deposit sum gives 797,836.82, or 797,837. The result agrees with the published answer key, 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 Growing Deposits and Withdrawals question

Setup

Use the first and thirtieth deposit amounts to infer the account yield: 5,000(1 + i)²⁹ = 50,000.

50000=5000(1+i)^{29}

Model

Each deposited amount grows at 3%, while earlier deposits also earn account interest for longer. Summing all terminal contributions gives a finite geometric-difference formula.

i=10^{1/29}-1=0.082637

Compute

The implied yield is 8.2637%, and substitution in the thirty-deposit sum gives 797,836.82, or 797,837.

F=5000\frac{(1+i)^{30}-1.03^{30}}{i-0.03}=797836.82

Answer

The calculation gives 797,837 for growing deposits and withdrawals, matching published choice C.

\boxed{F=797837\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 (760,694) does not match the checked growing deposits and withdrawals result (797,837); no distinct standard one-step error is identifiable.
BChoice B (783,948) does not match the checked growing deposits and withdrawals result (797,837); no distinct standard one-step error is identifiable.
DChoice D (805,541) does not match the checked growing deposits and withdrawals result (797,837); no distinct standard one-step error is identifiable.
EChoice E (821,379) does not match the checked growing deposits and withdrawals result (797,837); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: terminal fund from ten growing deposits

A laboratory deposits 1,000 at the end of year 1 and increases each later annual deposit by 3%, for ten deposits total. The fund earns 6% annually. Calculate the account value immediately after the tenth deposit.

A
13,987.65
B
14,442.18
C
14,897.71
D
15,317.80
E
15,802.33

Variant answer in brief

The closed-form difference quotient gives terminal value 14897.71. The fund reaches 14,897.71, which is choice C.

Setup

Deposit t has grown by 3% from the initial deposit and earns account interest for 10 − t years.

D_t=1000(1.03)^{t-1},\quad t=1,\ldots,10

Model

The terminal contributions form a mixed-growth geometric sum with account rate 6% and deposit growth 3%.

F_{10}=1000\sum_{t=1}^{10}(1.03)^{t-1}(1.06)^{10-t}

Compute

The closed-form difference quotient gives terminal value 14897.71.

F_{10}=1000\frac{1.06^{10}-1.03^{10}}{0.06-0.03}=14897.710573

Answer

The fund reaches 14,897.71, which is choice C.

\boxed{F_{10}=14897.71\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #83 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Growing Deposits and Withdrawals question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: terminal fund from ten growing deposits

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution