This Exam FM sample reference tests Forward Rate from Spot Rates. Solving f = 1.052³/1.05² − 1 gives 0.056, so the forward rate is 5.6%. The result agrees with the published answer key, choice E.
How to solve this Forward Rate from Spot Rates question
Setup
Setup
Let s₂ = 5.0% and s₃ = 5.2% be the annual effective spot rates for maturities two and three. The unknown f is the one-year rate earned between those maturities.
s2=0.050,s3=0.052
Model
Model
No-arbitrage requires a three-year spot investment to match a two-year spot investment followed by the one-year forward investment.
(1+s3)3=(1+s2)2(1+f)
Compute
Compute
Solving f = 1.052³/1.05² − 1 gives 0.056, so the forward rate is 5.6%.
f=1.0523/1.052−1=0.056
Answer
Answer
The calculation gives 0.056 for forward rate from spot rates, matching published choice E.
f=5.6%(E)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (0.048) does not match the checked forward rate from spot rates result (0.056); no distinct standard one-step error is identifiable.
BChoice B (0.050) does not match the checked forward rate from spot rates result (0.056); no distinct standard one-step error is identifiable.
CChoice C (0.052) does not match the checked forward rate from spot rates result (0.056); no distinct standard one-step error is identifiable.
DChoice D (0.054) does not match the checked forward rate from spot rates result (0.056); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: one-year forward rate implied by years three and four
A municipal curve quotes annual effective spot rates of 4.0% for three years and 4.5% for four years. Calculate the one-year forward rate for the fourth year that is consistent with these two zero-coupon prices.
A 4.00%
B 4.50%
C 5.51%
D 6.01%
E 6.53%
Variant answer in brief
The accumulation-factor ratio is 1.060145, so the implied forward rate is 6.01%. The forward rate is 6.01%, corresponding to choice D.
Setup
Setup
Use the three-year and four-year spot accumulations; the unknown rate applies only during year 4.
s3=0.040,s4=0.045
Model
Model
No-arbitrage equates a four-year spot investment with a three-year spot investment rolled forward for one additional year.
(1+s4)4=(1+s3)3(1+f3,4)
Compute
Compute
The accumulation-factor ratio is 1.060145, so the implied forward rate is 6.01%.
f3,4=1.0431.0454−1=0.060145
Answer
Answer
The forward rate is 6.01%, corresponding to choice D.
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