Verified solution · Exam FM
This Exam FM sample reference tests Prospective Loan Balances. Immediately after year 5, the balance is the value of ten payments in years 11–20. Immediately after year 15, five payments remain. Both values round to 378, so their absolute difference rounds to 0, choice A.
Independent solution
Setup
Use prospective balances; the payment holiday only changes the deferral of the remaining scheduled payments.
Model
At time 5 the ten later payments begin six years afterward. At time 15, five annual payments remain.
Compute
The special rate makes the two quantities nearly equal.
Answer
The requested whole-number difference is 0, choice A.
Continue without hunting through PDFs
The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
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 scheduled to be repaid by 20 annual end-of-year payments of 1,200 at 5% effective annually. Immediately after the fourth payment, the lender permits the borrower to skip the payments at the ends of years 5 and 6 while interest continues to accrue. What is the balance immediately after year 6?
After payment 4 the prospective balance is 1200 times a-angle-16. Accumulating this balance through the two-payment holiday gives 14338.37, choice D.
Setup
Immediately after the fourth scheduled payment, sixteen original payments remain.
Model
No cash leaves the loan during years 5 and 6, so the full balance accrues for two years.
Compute
Evaluate the prospective balance and the holiday accumulation.
Answer
The year-6 balance is 14338.37, choice D.
Calculator reproduction
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 83 Exam FM loans practice problems.
Continue in syllabus order
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam FM Sample Question #433 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
