Verified solution · Exam FM
This Exam FM sample reference tests Geometrically Increasing Loan Payments. The initial payment is 2584.39 from the ten-payment growing-annuity loan equation. After payment 8 only payments 9 and 10 remain; their value at time 8 is 7353.15, choice C.
Independent solution
Setup
Let X be the first year-end payment. Payment k is X times 1.06 to the k minus one.
Model
Price all ten payments at the 10% loan rate.
Compute
The equation gives X = 2584.391. Value the final two payments immediately after payment 8.
Answer
The outstanding balance is approximately 7353, choice C.
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 borrower promises eight annual payments, beginning with 3,000 at the end of year 1. Each later payment is 3% smaller than the preceding one. At a 5% annual effective loan rate, determine the original principal advanced.
Discounting the eight payments 3000 times 0.97 to successive powers at 5% gives an original principal of 17607.44, choice D.
Setup
Payment k equals 3000 times 0.97 to the k minus one.
Model
The principal is the present value of all eight promised payments.
Compute
Evaluate the finite geometric series.
Answer
The loan principal is 17607.44, choice D.
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 #323 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
