Verified solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. A zero NPV at 4% means the original 4,000 must grow to the same year-3 value as the three receipts reinvested at i. Solving the resulting quadratic gives positive rate 6.97%, so choice E is correct.
Independent solution
Setup
Move all values to year 3: the initial investment grows at the 4% evaluation rate.
Model
The three 1,400 receipts have two, one, and zero years of reinvestment at i.
Compute
The positive root of the quadratic is i = 6.968059%.
Answer
The reinvestment rate is approximately 7.0%, selecting choice E.
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Error diagnosis
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Original practice · fully worked
An investment costs 5,000 today and pays 1,200 at year 1 and 1,500 at year 2. Those receipts can be reinvested at 5%. Calculate the year-3 receipt required for the investment to earn a 6% annual terminal-value return over three years.
The target year-3 fund is 5,955.08. After crediting the reinvested first two receipts, the required final receipt is 3,057.08, choice D.
Setup
Accumulate the original cost at the target return to obtain the required year-3 wealth.
Model
Accumulate the first receipt for two years and the second for one year at the available reinvestment rate.
Compute
Solving the terminal balance gives final receipt 3057.08.
Answer
The year-3 receipt must be 3,057.08, which is choice D.
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ActuaryProof. “SOA Exam FM Sample Question #241 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
