Verified solution · Exam FM

SOA Exam FM Sample Question #65 Solution

This Exam FM sample reference tests Annuity Exhaustion Drop Payment. The fund is 50,382.16. Solving the withdrawal equation gives the final payment X = 1,430. 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 Annuity Exhaustion Drop Payment question

Setup

Accumulate the twenty beginning-of-year deposits at 8.16% to the withdrawal date. Withdrawals of 3,000 begin immediately, so they form an annuity-due.

F=1000\ddot s_{\overline{20}|\,0.0816}=50382.16

Model

Value the first twenty-six withdrawals plus the final drop payment at the same date. The drop payment occurs one period after the last full payment and is discounted accordingly.

50382.16=3000\ddot a_{\overline{26}|\,0.04}+X(1.04)^{-26}

Compute

The fund is 50,382.16. Solving the withdrawal equation gives the final payment X = 1,430.

X=1430

Answer

The calculation gives 1430 for annuity exhaustion drop payment, matching published choice C.

\boxed{X=1430\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 20 N; 8.16 I/Y; 1000 +/- PMT; 0 PV; 2nd PMT; 2nd SET; 2nd QUIT; CPT FV50382.16BGN mode for the deposits.

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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 (561) does not match the checked annuity exhaustion drop payment result (1430); no distinct standard one-step error is identifiable.
BChoice B (1226) does not match the checked annuity exhaustion drop payment result (1430); no distinct standard one-step error is identifiable.
DChoice D (1488) does not match the checked annuity exhaustion drop payment result (1430); no distinct standard one-step error is identifiable.
EChoice E (2240) does not match the checked annuity exhaustion drop payment result (1430); no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: final drop withdrawal from a pre-funded account

A fund contains 9640.52 at time 0. It pays 1,000 at the beginning of each year for twelve years, followed by one smaller payment at time 12. The fund earns 5% annually and is exhausted by the final payment. Calculate that final payment.

A
400
B
500
C
600
D
700
E
800

Variant answer in brief

Subtracting the full-withdrawal value and accumulating the residual twelve years gives 600. The final withdrawal is 600, which selects choice C.

Setup

Value the twelve full beginning-of-year withdrawals as an annuity-due at time 0.

F_0=9640.52,\quad i=0.05

Model

The final drop payment occurs at time 12, so add its discounted value and equate the total to the initial fund.

F_0=1000\ddot a_{\overline{12}|0.05}+X(1.05)^{-12}

Compute

Subtracting the full-withdrawal value and accumulating the residual twelve years gives 600.

X=[F_0-1000\ddot a_{\overline{12}|0.05}](1.05)^{12}=600

Answer

The final withdrawal is 600, which selects choice C.

\boxed{X=600\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 12 N; 5 I/Y; 1000 PMT; 2nd PMT; 2nd SET; 2nd QUIT; CPT PV−8863.25BGN mode for the twelve full withdrawals; use the displayed equation for the residual.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #65 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuity Exhaustion Drop Payment 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: final drop withdrawal from a pre-funded account

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