This Exam FM sample reference tests Forward Rate from Spot Curve. Solving 1 + f = 1.095⁵/1.09⁴ gives f = 0.115, or 11.5%. The result agrees with the published answer key, choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (9.5%) does not match the checked forward rate from spot curve result (11.5%); no distinct standard one-step error is identifiable.
BChoice B (10.0%) does not match the checked forward rate from spot curve result (11.5%); no distinct standard one-step error is identifiable.
DChoice D (12.0%) does not match the checked forward rate from spot curve result (11.5%); no distinct standard one-step error is identifiable.
EChoice E (12.5%) does not match the checked forward rate from spot curve result (11.5%); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: three-year forward rate between years two and five
The two-year annual effective spot rate is 3.5% and the five-year annual effective spot rate is 5.0%. Calculate the constant annual effective forward rate for the three-year interval from time 2 to time 5.
A 4.00%
B 5.00%
C 5.52%
D 6.01%
E 6.52%
Variant answer in brief
Taking the cube root of the residual accumulation gives 6.01% per year. The three-year forward rate is 6.01%, corresponding to choice D.
Setup
Setup
The unknown rate applies for three years, after the initial two-year spot investment.
s2=0.035,s5=0.050
Model
Model
Equate the five-year spot accumulation to two years at the two-year spot rate followed by three years at the forward rate.
(1.05)5=(1.035)2(1+f)3
Compute
Compute
Taking the cube root of the residual accumulation gives 6.01% per year.
f=[1.03521.055]1/3−1=0.060121
Answer
Answer
The three-year forward rate is 6.01%, corresponding to choice D.
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