Verified solution · Exam FM

SOA Exam FM Sample Question #462 Solution

This Exam FM sample reference tests Retrospective Loan Balance. The half-year rate is 3.25%. Accumulating the original principal for ten periods and subtracting the accumulated value of ten payments gives an outstanding balance of 3367821.18, choice D.

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 Retrospective Loan Balance question

Setup

Align all quantities to the semiannual payment period.

j=0.065/2=0.0325

Model

Use the retrospective balance immediately after the tenth payment.

B_{10}=5{,}000{,}000(1+j)^{10}-303{,}244.53s_{\overline{10}|j}

Compute

Evaluate the accumulated loan and accumulated payments at the same date.

B_{10}=3{,}367{,}821.18

Answer

The outstanding balance rounds to 3367821, choice D.

\boxed{B_{10}\approx3{,}367{,}821\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM; 10 · N; 3.25 · I/Y; 5000000 · PV; 303244.53 · +/− · PMT; CPT · FV−3,367,821.18The magnitude is the balance after payment 10.

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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 subtracts ten unaccumulated payments from the accumulated principal.
BChoice B uses 6.5% as the rate each half-year and over-credits the payment stream relative to principal.
CChoice C computes principal minus ten payments without including any interest.
EChoice E accumulates the principal but discounts the payments back to time zero instead of accumulating them to time 10.

Original practice · fully worked

Original variant: payment for a target balance

A business borrows 500,000 at 3% effective per half-year. It makes six equal end-of-half-year payments and wants the balance immediately after the sixth payment to be exactly 400,000. Determine the semiannual payment.

A
24,105.33
B
27,384.10
C
30,459.75
D
33,333.33
E
36,917.42

Variant answer in brief

A retrospective balance equation at time 6 gives payment equal to the accumulated principal minus 400000, divided by s-angle-6. The result is 30459.75, choice C.

Setup

Accumulate the original loan and all six payments to the date immediately after payment 6.

400{,}000=500{,}000(1.03)^6-Ps_{\overline6|0.03}

Model

Isolate the level payment.

P=\frac{500{,}000(1.03)^6-400{,}000}{s_{\overline6|0.03}}

Compute

Evaluate the six-period accumulation factor.

P=30{,}459.7500

Answer

The required semiannual payment is 30459.75, choice C.

\boxed{P=30{,}459.75\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

6 · N; 3 · I/Y; 500000 · PV; 400000 · +/− · FV; CPT · PMT−30,459.75The opposite signs for PV and target FV represent the outstanding balance convention.

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #462 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Retrospective Loan Balance 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: payment for a target balance

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