This Exam FM sample reference tests Spot and Forward Rates. The first bond leaves 59.31 after the year-1 payment, while the second bond leaves a year-2 shortfall of 63.87. The surplus must earn 7.69%, so the keyed answer is E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (6.0) does not satisfy the year-2 cash-balance equation after reinvesting the exact year-1 surplus; no distinct standard one-step error is identifiable.
BChoice B (6.6) does not satisfy the year-2 cash-balance equation after reinvesting the exact year-1 surplus; no distinct standard one-step error is identifiable.
CChoice C (7.0) does not satisfy the year-2 cash-balance equation after reinvesting the exact year-1 surplus; no distinct standard one-step error is identifiable.
DChoice D (7.3) does not satisfy the year-2 cash-balance equation after reinvesting the exact year-1 surplus; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: one-year bond allocation required to close a later shortfall
A reserve must pay 1,000 at year 1 and 1,100 at year 2. A two-year zero-coupon holding will provide 950 at year 2. Money remaining after the first payment can earn 6% for year 2. How much must be invested today in a one-year zero-coupon bond yielding 5%?
A 924.08
B 978.44
C 1,032.79
D 1,087.15
E 1,141.51
Variant answer in brief
The year-2 bond leaves a shortfall of 150, requiring 141.51 at year 1. The one-year bond must therefore mature to 1,141.51, so its initial cost is 1,087.15, choice D.
Setup
Setup
Work backward from year 2 to find the surplus that must remain immediately after the year-1 payment.
S1(1.06)=1100−950
Model
Model
The one-year bond must mature to the first liability plus that required surplus.
1.05X=1000+S1
Compute
Compute
The required year-1 surplus is 141.51, giving an initial one-year bond investment of 1087.15.
X=1.051000+150/1.06=1087.151842
Answer
Answer
The required investment is 1087.15, which is choice D.
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.
