Worked solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. Paul's two-year yield is 9.5445%. The combined 10% terminal-value equation implies Toby receives Z = 236.00, and Toby's own cash-flow equation gives yield 11.5549%. The difference is 2.01%, choice C.
Independent solution
Setup
Solve Paul's two-year yield from his single investment and receipt.
Model
Use the combined 10% terminal-value equation to determine Toby's final receipt.
Compute
This gives Z = 236.00. Solving Toby's two-deposit equation gives Y = 11.554944% and Y − X = 2.0104%.
Answer
The yield difference is approximately 2%, selecting choice C.
Test the method on unseen problems
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
Investor A deposits 400 today and receives 500 at year 2. Investor B deposits 100 today and another 100 at year 1, then receives 230 at year 2. Calculate the annual effective yield on the combined cash flows.
At year 2, the combined receipts are 730. Equating that to the accumulated 500 initial deposit plus the year-1 deposit gives annual effective yield 11.24%, choice C.
Setup
Combine cash flows at each date rather than averaging individual yields.
Model
Use year 2 as the comparison date for the combined investment.
Compute
The positive root is j = 11.243557%.
Answer
The combined annual effective yield is 11.24%, selecting choice C.
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