Verified solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. The 5% level-payment option totals 2407.28. Under 75-per-year constant principal, the opening balances sum to 15750, so total payments are 1,500 plus i times that sum. Equating totals gives i = 5.76%, choice C.
Independent solution
Setup
Compute the level annual payment and total under option 1.
Model
Under option 2, total principal is 1,500 and total interest is i times the arithmetic sequence of opening balances.
Compute
The balance sum is 15750. Equating T2 to 2407.28 gives i = 5.760493%.
Answer
The annual rate under option 2 is approximately 5.76%, selecting choice C.
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Original practice · fully worked
A 20,000 loan is repaid over eight years. Option A uses level annual payments at 3%. Option B repays 2,500 principal each year plus interest on the opening balance. Find Option B's annual rate if its total payments must exceed Option A's total by exactly 500.
Option A's total is 22,793.02. Setting principal plus interest on the eight opening balances equal to that total plus 500 gives Option B rate 3.66%, choice A.
Setup
Compute the eight-payment total under the 3% level-payment option.
Model
Under constant principal, add 20,000 to interest on the eight opening balances and impose the 500 premium.
Compute
The level total is 22793.02, and solving gives i = 3.658914%.
Answer
Option B's annual rate is 3.66%, selecting choice A.
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ActuaryProof. “SOA Exam FM Sample Question #289 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
