Verified solution · Exam FM
This Exam FM sample reference tests Loan Amortization. Valuing the first five payments at 11% and the last five at 12% deferred five years gives factor 5.83516; hence X = 20,000/5.83516 = 3,427.50, choice C.
Independent solution
Setup
Split the ten repayments at the interest-rate change after year five.
Model
The first block uses the 11% annuity factor; the second block uses 12% at its local date and is then discounted through the first five years at 11%.
Compute
The combined present-value factor is 5.83516, giving a payment of 3,427.50.
Answer
Therefore the annual payment is 3,427.50, choice C.
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Error diagnosis
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Original practice · fully worked
A bakery borrows 12,000 and repays it with eight equal year-end payments. Interest is 5% effective for the first four years and 7% effective for the last four. Find the level payment.
The two four-payment blocks have combined value factor 6.33262, giving 1,894.95, choice C.
Setup
Partition the payments where the contractual rate changes.
Model
Value the later four-payment annuity at year four using 7%, then discount that value to the loan date through the 5% period.
Compute
Adding the early block gives a total factor of 6.3326176.
Answer
The level annual payment is 1,894.95, which is choice C.
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Drill the method: Exam FM Loan Amortization and Balances problems
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ActuaryProof. “SOA Exam FM Sample Question #127 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
