Verified solution · Exam FM
This Exam FM sample reference tests Equivalent Interest Measures. Equating the nominal-discount accumulation with the force-of-interest accumulation gives n = 16.568 years, which rounds to choice B.
Independent solution
Setup
A 12% nominal discount rate convertible quarterly has quarterly discount rate 3%, so each quarter accumulates by 1 divided by 0.97.
Model
Equate the two account balances after n years. Fund X has 4n quarterly periods, and Fund Y accumulates under force 0.08.
Compute
Take natural logarithms and isolate n.
Answer
The balances meet after approximately 16.6 years, so the answer is B.
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Original practice · fully worked
Fund A earns a nominal annual discount rate of 8% convertible semiannually. Fund B receives 500 and earns a constant force of interest of 6%. Determine the deposit in Fund A that makes the two balances equal exactly seven years from now.
Equating the seven-year accumulation factors gives an initial Fund A deposit of 429.71, which is choice C.
Setup
The half-year discount rate in Fund A is 4%, so its half-year accumulation factor is 1 divided by 0.96.
Model
Seven years contain 14 half-years. Equate Fund A's accumulated deposit X to Fund B's force-of-interest balance.
Compute
Move Fund A's accumulation factor to the other side and evaluate.
Answer
The required initial deposit is approximately 429.71, so choice C is correct.
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ActuaryProof. “SOA Exam FM Sample Question #214 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
