Worked solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. Equating the five-year spot accumulation to the four-year spot accumulation followed by the fifth-year forward factor gives 11.52%, which corresponds to choice E.
Independent solution
Setup
Use only the four- and five-year spot rates because they bracket the one-year forward period being requested.
Model
No-arbitrage requires the direct five-year accumulation and the rolled four-year investment to agree.
Compute
Isolating the final one-year factor gives forward rate 11.52%.
Answer
The implied fifth-year rate is approximately 11.5%, so choice E is correct.
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30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
The three-year annual effective spot rate is 4%. The one-year forward rate applying only during year 4 is 6%. Under no arbitrage, calculate the four-year annual effective spot rate.
The four-year accumulation factor is the three-year spot factor multiplied by 1.06. Taking its fourth root gives a four-year spot rate of 4.50%, choice A.
Setup
Build the four-year accumulation by rolling the three-year spot investment through the known fourth-year forward period.
Model
Take the fourth root to convert the total four-year factor to an annual effective spot rate.
Compute
The annualized four-year spot rate is 4.4964%.
Answer
The four-year spot rate is 4.50%, selecting choice A.
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