Verified solution · Exam FM

SOA Exam FM Sample Question #177 Solution

This Exam FM sample reference tests Loan Amortization. The original loan value is 8,498.35 and the balance after five payments is 7,581.57; only 916.78 of the first 5,000 paid is principal, so interest is 4,083.22, 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 Loan Amortization question

Setup

Price both tiers of repayments at loan issue to obtain the amount originally advanced.

L=1000a_{\overline{5}|\,0.10}+2000v^5a_{\overline{5}|\,0.10}=8498.35

Model

Immediately after the fifth payment, the balance is the present value of the five remaining larger payments.

B_5=2000a_{\overline{5}|\,0.10}=7581.57

Compute

The decline in balance is principal repaid; subtract that amount from the first five total payments to isolate interest.

I_{1:5}=5000-(L-B_5)=4083.22

Answer

Interest contained in the first five payments is 4,083.22, which is choice D.

\boxed{I_{1:5}=4083.22\quad\text{(D)}}

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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 is inconsistent with the original-value minus prospective-balance principal calculation; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the original-value minus prospective-balance principal calculation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the original-value minus prospective-balance principal calculation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the original-value minus prospective-balance principal calculation; no distinct standard single-step error producing it is identifiable.

Original practice · fully worked

Original variant: interest paid during a stepped repayment plan

A loan is repaid over eight years with 500 at each of years 1 through 4 and 800 at each of years 5 through 8. At 7% effective annually, determine the total interest contained in the first four payments.

A
748.89
B
848.89
C
948.89
D
1,051.11
E
1,251.11

Variant answer in brief

The loan value is 3,760.88 and the year-four balance is 2,709.77, so first-four interest is 948.89, choice C.

Setup

Value both repayment tiers at issue to determine the loan principal.

L=500a_{\overline{4}|\,0.07}+800v^4a_{\overline{4}|\,0.07}=3760.8754

Model

After the fourth payment, the remaining obligation consists only of four payments of 800.

B_4=800a_{\overline{4}|\,0.07}=2709.7690

Compute

Principal repaid is the balance decline of 1,051.1064; the rest of the first 2,000 paid is interest.

I_{1:4}=2000-(3760.8754-2709.7690)=948.8936

Answer

The first four payments contain 948.89 of interest, corresponding to choice C.

\boxed{I_{1:4}=948.89\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #177 — 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

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: interest paid during a stepped repayment plan

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution