Worked 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.
Test the method on unseen problems
30 original loans problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
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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