Verified solution · Exam FM

SOA Exam FM Sample Question #285 Solution

This Exam FM sample reference tests Annuities. The 20 beginning-of-year deposits accumulate to 57485.26. The 360-payment monthly annuity-due costs 57450.21 at 10% nominal convertible monthly, leaving 35.06; 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 Annuities question

Setup

Accumulate the twenty annual beginning-of-year deposits to time 20.

F_{20}=1000\ddot s_{\overline{20}|0.0925}

Model

Value the 30-year monthly annuity-due at the monthly rate 10% divided by 12.

C=500\ddot a_{\overline{360}|0.10/12}

Compute

The fund is 57485.26 and the purchase cost is 57450.21, leaving 35.0574.

F_{20}-C=35.05741411

Answer

The remaining balance is approximately 35, selecting choice C.

\boxed{B\approx35\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 2ND · PMT · 2ND · SET · 20 · N · 9.25 · I/Y · 0 · PV · 1000 · +/- · PMT · CPT · FVFV = 57485.26BGN mode for annual deposits.
360 · N · 0.833333 · I/Y · 0 · FV · 500 · PMT · CPT · PVPV = -57450.21Remain in BGN mode for the annuity-due.

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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 does not satisfy the difference between the accumulated annual deposits and monthly annuity-due purchase price; no distinct standard one-step error is identifiable.
BChoice B (0) does not satisfy the difference between the accumulated annual deposits and monthly annuity-due purchase price; no distinct standard one-step error is identifiable.
DChoice D (370) does not satisfy the difference between the accumulated annual deposits and monthly annuity-due purchase price; no distinct standard one-step error is identifiable.
EChoice E (510) does not satisfy the difference between the accumulated annual deposits and monthly annuity-due purchase price; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: annual beginning-of-year deposit required to buy a monthly annuity

A saver deposits the same amount at the beginning of each year for 15 years into a fund earning 8% annually. At time 15 the fund must buy a 20-year annuity-due paying 300 monthly, priced at 9% nominal interest convertible monthly. Calculate the annual deposit.

A
916.47
B
973.75
C
1,031.03
D
1,088.31
E
1,145.59

Variant answer in brief

The monthly annuity-due costs 33,593.56 at time 15. Dividing that target by the 15-deposit accumulated annuity-due factor gives annual deposit 1,145.59, choice E.

Setup

Value the 240 monthly payments at time 15 using the monthly rate 9% divided by 12.

C=300\ddot a_{\overline{240}|0.09/12}

Model

The fifteen annual beginning-of-year deposits must accumulate to exactly that cost.

D\ddot s_{\overline{15}|0.08}=C

Compute

The annuity cost is 33593.56, giving deposit 1145.59.

D=1145.58853176

Answer

The required annual deposit is 1,145.59, selecting choice E.

\boxed{D\approx1145.59\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 2ND · PMT · 2ND · SET · 240 · N · 0.75 · I/Y · 0 · FV · 300 · PMT · CPT · PVPV = -33593.56BGN mode.
15 · N · 8 · I/Y · 0 · PV · 1 · +/- · PMT · CPT · FVFV factor = 29.324283

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #285 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities 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: annual beginning-of-year deposit required to buy a monthly annuity

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