Worked solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. Discounting each dated cash flow at its matching spot rate gives present-value components of 9.62, 10.99, 12.77, and 15.26. Their sum is 48.64, choice B.
Independent solution
Setup
Use a different discount factor for each maturity because the table gives a term structure, not one flat yield.
Model
Insert the four cash flows and their maturity-specific spot rates.
Compute
The four discounted amounts sum to 48.6363.
Answer
The investment is worth approximately 48.64 at the start, so choice B is correct.
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
A portfolio pays 500 at year 1, 800 at year 2, and 1,000 at year 3. The one- and two-year spot rates are 3% and 4%. Its present value is 2088.92. Calculate the three-year annual effective spot rate.
The first two payments contribute 1225.08 of present value. The remaining value assigned to the year-3 payment implies a three-year spot rate of 5.00%, choice B.
Setup
Remove the known present values of the first two payments from the quoted total price.
Model
The residual must equal the discounted year-3 payment at the unknown three-year spot rate.
Compute
Solving the residual discount factor gives annual spot rate 5.0000%.
Answer
The three-year spot rate is 5.00%, selecting choice B.
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