Verified solution · Exam FM
This Exam FM sample reference tests Unit-Payment Loan Amortization Identities. The loan advances a-angle-n and receives total payments n. Since all principal repaid equals the initial loan, total interest is n minus a-angle-n; therefore choice A is true.
Independent solution
Setup
The time-zero principal of a unit-payment n-period loan is the annuity-immediate value.
Model
The borrower makes n payments of one, so the undiscounted total paid is n.
Compute
Total paid decomposes into principal repaid plus interest paid.
Answer
This identity is precisely choice A.
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Error diagnosis
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Original practice · fully worked
A loan is amortized by payments of 1 at each period-end for n periods at rate i. With v equal to 1/(1+i), which expression gives the principal repaid in payment t?
Immediately before payment t, the balance is a-angle-(n−t+1). Subtracting its interest portion from 1 gives principal v to the n−t+1, choice B.
Setup
There are n minus t plus one payments remaining immediately before payment t.
Model
The interest portion of payment t is i times that balance.
Compute
Principal is payment minus interest; use one minus i a-angle-m equals v to the m.
Answer
The correct expression is choice B.
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ActuaryProof. “SOA Exam FM Sample Question #364 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
