Verified solution · Exam FM

SOA Exam FM Sample Question #392 Solution

This Exam FM sample reference tests Annuities and Perpetuities. The five deposits supply 1,000 of principal; accumulating their separately transferred interest at 6% gives an additional factor 16.2553 times 200i, and the target 1,260 implies i = 8%, choice A.

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 and Perpetuities question

Setup

Keep deposited principal separate from the annual interest transferred for reinvestment.

1260=5(200)+200i\sum_{k=1}^{5}k(1.06)^{5-k}

Model

At year k, interest is based on k deposits and then grows at 6% for the remaining years.

1260=1000+200i(16.2553)

Compute

The accumulated transfer factor is 16.2553, making the source interest rate 8%.

i=\frac{260}{3251.06}=0.08

Answer

The deposits earn 8.00% before transfer, corresponding to choice A.

\boxed{i=8.00\%\quad\text{(A)}}

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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.

BChoice B is inconsistent with the principal-plus-reinvested-interest accumulation equation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the principal-plus-reinvested-interest accumulation equation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the principal-plus-reinvested-interest accumulation equation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the principal-plus-reinvested-interest accumulation equation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: terminal value of a separately reinvested interest plan

A museum deposits 200 at the beginning of each of six years. Principal earns 9% simple interest each year, with every year's interest transferred to an account earning 7% annually. Find the combined value at the end of year 6.

A
1,425.32
B
1,525.32
C
1,625.32
D
1,725.32
E
1,825.32

Variant answer in brief

The six deposits provide 1,200 principal and the accumulated interest transfers provide 425.32, totaling 1,625.32, choice C.

Setup

Track fixed principal and transferred interest in separate accounts.

V_6=6(200)+\sum_{k=1}^{6}(0.09)(200k)(1.07)^{6-k}

Model

At year k, source principal is 200k and its 9% interest grows at 7% until year six.

V_6=1200+425.3197

Compute

The transfers accumulate to 425.3197 in addition to 1,200 principal.

V_6=1625.3197

Answer

The combined terminal value is 1,625.32, corresponding to choice C.

\boxed{V_6=1625.32\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #392 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Annuities and Perpetuities question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: terminal value of a separately reinvested interest plan

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution