Worked solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. A four-year 5% spot investment must equal a two-year 4% spot investment rolled for two additional years at the implied rate. Solving the two-year forward factor gives 6.01%, so choice E is correct.
Independent solution
Setup
Use the two- and four-year spot rates that bracket the requested two-year forward interval.
Model
Equate direct four-year accumulation with two years at the spot rate followed by two years at forward rate f.
Compute
Taking the positive square root gives f = 6.009615%.
Answer
The implied two-year rate at year 2 is approximately 6.0%, selecting choice E.
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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 two-year annual effective spot rate is 3%. The implied annual effective rate for the two-year period from year 2 to year 4 is 5%. Calculate the four-year annual effective spot rate.
Two years at 3% followed by two years at 5% gives the four-year accumulation. Taking its fourth root yields four-year spot rate 4.00%, choice D.
Setup
Combine the two two-year accumulation blocks under no arbitrage.
Model
Take the fourth root; equivalently, take the square root of the product of the two annual factors.
Compute
The four-year spot rate is 3.995192%.
Answer
The four-year annual effective spot rate is 4.00%, selecting choice D.
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