Verified solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. Solving 150 = 100v + 80v² gives annual effective yield 13.6106%. Converting that annual accumulation factor to a quarterly nominal quote gives 12.97%, so choice B is correct.
Independent solution
Setup
Write the investment present-value equation in the annual discount factor v.
Model
Use the positive discount root to obtain the annual effective yield.
Compute
The annual effective rate is 13.610631%. Convert its accumulation factor to four equal quarters and multiply the quarterly rate by four.
Answer
The nominal annual rate convertible quarterly is approximately 13.0%, selecting choice B.
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Original practice · fully worked
An investor pays 200 today and receives 80 at year 1 plus X at year 2. The desired return is 12% nominal annually convertible quarterly. Calculate X.
The quarterly rate is 3%, giving annual effective factor 1.03 to the fourth. Discounting the two receipts at that annual factor and solving gives X = 163.31, choice C.
Setup
Convert the 12% nominal quarterly quote to its annual effective accumulation factor.
Model
Use the equivalent annual discount factor in the two-receipt present-value equation.
Compute
Solving for the year-2 receipt gives 163.31.
Answer
The required second receipt is 163.31, selecting choice C.
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ActuaryProof. “SOA Exam FM Sample Question #291 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
