Verified solution · Exam FM

SOA Exam FM Sample Question #288 Solution

This Exam FM sample reference tests Loan Balances and Amortization. At payment 5, the prospective balance before the extra payment is the value of ten remaining 400 payments. Subtracting 1,000 leaves 1944.03, which amortized over five years requires X = 461.51, 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 Loan Balances and Amortization question

Setup

Immediately after the scheduled fifth payment, ten original payments remain.

B_5^-=400a_{\overline{10}|0.06}

Model

Apply the extra 1,000 at that date and reamortize the remaining balance over five years.

B_5=B_5^--1000

B_5=Xa_{\overline5|0.06}

Compute

The post-extra balance is 1944.03, giving revised payment 461.506869.

X=461.50686872

Answer

The revised annual payment is approximately 461.51, selecting choice C.

\boxed{X\approx461.51\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 10 · N · 6 · I/Y · 0 · FV · 400 · PMT · CPT · PVPV = -2944.03
5 · N · 1944.03 · +/- · PV · CPT · PMTPMT = 461.51

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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 (264.13) does not satisfy the payment-5 balance after the extra 1,000 and its five-payment reamortization; no distinct standard one-step error is identifiable.
BChoice B (435.38) does not satisfy the payment-5 balance after the extra 1,000 and its five-payment reamortization; no distinct standard one-step error is identifiable.
DChoice D (556.46) does not satisfy the payment-5 balance after the extra 1,000 and its five-payment reamortization; no distinct standard one-step error is identifiable.
EChoice E (698.90) does not satisfy the payment-5 balance after the extra 1,000 and its five-payment reamortization; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: extra payment required to reach a target revised installment

Immediately after a scheduled payment, a 5% annual loan has eight remaining payments of 500. The borrower wants to make an extra payment now and then repay the reduced balance with five annual payments of 300. Calculate the extra payment.

A
1,546.21
B
1,642.85
C
1,739.49
D
1,836.13
E
1,932.76

Variant answer in brief

The original remaining balance is 3,231.61. The target five-payment schedule supports 1,298.84; their difference is extra payment 1,932.76, choice E.

Setup

Value the eight original remaining payments at the change date.

B=500a_{\overline8|0.05}

Model

Value the desired five-payment replacement schedule and subtract it from the old balance.

E=B-300a_{\overline5|0.05}

Compute

The two balances are 3231.61 and 1298.84, giving extra payment 1932.76.

E=1932.76337852

Answer

The required extra payment is 1,932.76, selecting choice E.

\boxed{E\approx1932.76\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 8 · N · 5 · I/Y · 0 · FV · 500 · PMT · CPT · PVPV = -3231.61
5 · N · 300 · PMT · CPT · PVPV = -1298.84

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #288 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Loan Balances and Amortization 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: extra payment required to reach a target revised installment

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