This Exam FM sample reference tests Bond Pricing. Subtracting the two bond-price equations eliminates the common redemption amount and gives 17 years, which is choice B.
Let v be the half-year discount factor and let 2n be the number of semiannual periods. The yield per half-year is 3.5%.
j=0.07/2=0.035
v=(1.035)−1
Model
Model
Bond X pays 50 more coupon each half-year, while Bond Y pays 50 more at redemption. Subtracting their prices removes the unknown common redemption value.
969.52=50a2n∣0.035−50v2n
969.52=0.03550(1−v2n)−50v2n
Compute
Compute
Isolating the maturity discount factor gives 0.3104696. Taking logarithms converts the number of half-years to years.
v2n=0.3104696
n=2ln(1.035)−ln(0.3104696)=17.0003
Answer
Answer
The bonds mature in 17 years, so the correct answer is choice B.
n=17(B)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A follows from treating 14 as the number of years after rounding the discount factor too early. The logarithmic solution uses all 34 semiannual periods.
CChoice C is not obtained from v to the power 2n equal to 0.3104696. The exponent counts half-years, not years.
DChoice D treats the 34 half-year periods as 34 years instead of dividing the period count by two.
EChoice E results from failing to subtract the 50 higher redemption amount. The coupon advantage and redemption disadvantage both belong in the price difference.
Original practice · fully worked
Original variant: redemption difference from paired bond prices
Two 12-year bonds have face amount 5,000, semiannual coupons, and a 6% nominal yield convertible semiannually. Bond A has a 5.0% annual coupon rate and redemption R. Bond B has a 4.4% annual coupon rate and redemption R plus D. If A costs 180 more than B, determine D.
A 120.5
B 135.0
C 150.5
D 166.8
E 181.2
Variant answer in brief
Subtracting the two price equations gives a redemption difference of 150.49, so the answer is choice C.
Setup
Setup
The half-year yield is 3%. Bond A's semiannual coupon exceeds Bond B's by 15.
j=0.03
N=24
ΔC=5000(0.050−0.044)/2=15
Model
Model
In the price difference, the coupon advantage of A is offset by its redemption being D lower.
180=15a24∣0.03−Dv24
Compute
Compute
The annuity factor is 16.93554 and v to the 24th power is 0.491934. Solving the linear equation gives 150.49.
D=0.49193415(16.93554)−180
D=150.4941
Answer
Answer
The redemption difference is approximately 150.5, which is choice C.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
