Verified solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. In a level-payment loan, principal and interest portions are equal when the discount factor for the remaining payments equals one-half. Solving v to the power 21 − t = 0.5 gives t = 6.79, nearest the 7th payment; choice B.
Independent solution
Setup
With t denoting the payment number, the principal portion is the payment discounted for the remaining-payment count.
Model
Set principal and interest equal, which makes each one-half of the level payment.
Compute
At 5%, solving gives t = 6.793301, so the nearest installment is 7.
Answer
The portions are most nearly equal in the 7th installment, selecting choice B.
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Error diagnosis
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Original practice · fully worked
A 25-payment level annual loan is designed so the principal and interest portions are equal in payment 10. Calculate the annual effective interest rate.
At payment 10, sixteen payments including the current one remain. Equality requires the sixteen-period discount factor to be one-half, giving annual rate 4.43%, choice E.
Setup
Count the payment-10 principal portion as the level payment discounted for sixteen periods.
Model
Equal principal and interest portions each equal one-half of the payment.
Compute
Solving the accumulation factor gives annual rate 4.427378%.
Answer
The annual effective rate is 4.43%, selecting choice E.
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Drill the method: Exam FM Loan Amortization and Balances problems
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ActuaryProof. “SOA Exam FM Sample Question #256 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
