Verified solution · Exam FM

SOA Exam FM Sample Question #370 Solution

This Exam FM sample reference tests Loan Amortization. Pricing the twenty quarterly repayments gives a quarterly effective rate of 1.5%; matching that factor to monthly compounding gives nominal annual rate 5.97%, 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 Loan Amortization question

Setup

Treat each quarter as one loan-payment period and solve its effective rate first.

5000=291.23a_{\overline{20}|\,i_q}

Model

The twenty-payment annuity equation has periodic rate 1.5%.

i_q=0.015

Compute

Three monthly factors must reproduce the quarterly factor; converting the resulting monthly rate to a nominal annual quote gives 0.059703.

\left(1+\frac{j}{12}\right)^3=1.015,\qquad j=0.059703

Answer

The nominal annual rate convertible monthly is 5.97%, corresponding to choice A.

\boxed{j\approx5.97\%\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

2nd CLR TVM; 20 N; 5000 PV; 291.23 +/- PMT; 0 FV; CPT I/YI/Y = 1.5000The displayed I/Y is the effective rate per quarter. Convert its three-month factor to a monthly rate, then multiply by 12.

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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 quarterly annuity equation and three-month accumulation conversion; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the quarterly annuity equation and three-month accumulation conversion; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the quarterly annuity equation and three-month accumulation conversion; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the quarterly annuity equation and three-month accumulation conversion; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: loan amount supported by a monthly nominal quote

A cooperative can pay 300 at each quarter-end for five years. Interest is 6% nominal annually convertible monthly. What amount can it borrow today?

A
4,846.78
B
4,996.78
C
5,146.78
D
5,296.78
E
5,446.78

Variant answer in brief

The monthly quote implies a quarterly rate of 1.5075%; discounting twenty payments gives a loan amount of 5,146.78, choice C.

Setup

Convert the monthly nominal quote to the effective rate over one quarterly payment period.

i_q=(1+0.06/12)^3-1=0.015075125

Model

The amount advanced is the present value of twenty level quarter-end payments.

L=300a_{\overline{20}|\,i_q}

Compute

Evaluating the annuity factor gives 5,146.7793.

L=5146.7793

Answer

The cooperative can borrow 5,146.78, corresponding to choice C.

\boxed{L=5146.78\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

2nd CLR TVM; 20 N; 1.5075125 I/Y; 300 +/- PMT; 0 FV; CPT PVPV = 5146.78

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #370 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Loan 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: loan amount supported by a monthly nominal quote

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