Verified solution · Exam FM
This Exam FM sample reference tests Loan Amortization. Equating the original 15-payment value to the revised ten-year stream gives 50a₁₅ = 50a₁₀ + 30v⁵a₅; accumulating to year 10 produces the expression in choice C.
Independent solution
Setup
The original loan value is the present value of 15 payments of 50.
Model
Under the revision, the regular ten payments remain and the additional 30 occurs with payments six through ten.
Compute
Equate the two streams at time zero, then multiply through by the ten-year accumulation factor to match the answer format.
Answer
The resulting accumulated-value equation is the one in choice C.
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Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A twelve-year loan at 5% has annual payments of 100. The borrower instead pays 100 in years 1–3 and 100+X in years 4–8, fully repaying at year 8. Determine X.
Equating the original 12-year value to the revised eight-year stream gives X = 64.17, choice C.
Setup
Keep the original loan value fixed and compare the two complete repayment streams at the loan date.
Model
The extra amount occurs only in years four through eight, a five-payment annuity deferred three years.
Compute
The value gap between the original and shortened base streams divided by that deferred factor is 64.1728.
Answer
Each of the last five payments must increase by 64.17, choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 83 Exam FM loans practice problems.
Drill the method: Exam FM Loan Amortization and Balances problems
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ActuaryProof. “SOA Exam FM Sample Question #168 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
