Verified solution · Exam FM

SOA Exam FM Sample Question #296 Solution

This Exam FM sample reference tests Loan Balances and Amortization. The first balance equation gives monthly rate 1.2%. A 50,000 loan with payments 800 at that rate has exact term 116.22, so 116 full payments are followed by a drop payment numbered 117; choice B.

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

Use the first payment and resulting balance to infer the monthly interest rate.

50000(1+j)-800=49800

j=0.01200000

Model

Solve the level-payment annuity term at the recovered monthly rate.

50000=800a_{\overline n|0.012}

Compute

The exact term is 116.216299. Because it is not an integer, the final drop payment occurs at the next payment number, 117.

N=\lceil116.21629923\rceil=117

Answer

The loan is retired with payment 117, selecting choice B.

\boxed{N=117\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

2ND · CLR TVM · 1.2 · I/Y · 50000 · +/- · PV · 800 · PMT · 0 · FV · CPT · NN = 116.22Round up to include the final drop payment.

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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 (115) does not satisfy the first-payment balance rate and the ceiling of the exact annuity term; no distinct standard one-step error is identifiable.
CChoice C (119) does not satisfy the first-payment balance rate and the ceiling of the exact annuity term; no distinct standard one-step error is identifiable.
DChoice D (121) does not satisfy the first-payment balance rate and the ceiling of the exact annuity term; no distinct standard one-step error is identifiable.
EChoice E (123) does not satisfy the first-payment balance rate and the ceiling of the exact annuity term; no distinct standard one-step error is identifiable.

Original practice · fully worked

Original variant: final drop payment from a noninteger monthly amortization term

A 30,000 loan charges 1% per month and is repaid by 600 at each month-end, followed by a smaller final drop payment. Calculate the amount of the final drop payment.

A
357.39
B
377.24
C
397.10
D
416.95
E
436.81

Variant answer in brief

The exact term is 69.66 months, so 69 full payments are made. Accumulating the remaining balance one month gives final drop payment 397.10, choice C.

Setup

Solve the exact level-payment term to identify the number of full 600 payments.

30000=600a_{\overline n|0.01}

Model

The exact term lies between 69 and 70; compute the balance immediately after 69 full payments.

B_{69}=30000(1.01)^{69}-600s_{\overline{69}|0.01}

Compute

The remaining balance grows one more month to final payment 397.10.

D=B_{69}(1.01)=397.09894814

Answer

The final drop payment is 397.10, selecting choice C.

\boxed{D\approx397.10\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2ND · CLR TVM · 1 · I/Y · 30000 · +/- · PV · 600 · PMT · 0 · FV · CPT · NN = 69.66

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #296 — 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: final drop payment from a noninteger monthly amortization term

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