This Exam FM sample reference tests Annuities and Perpetuities. Canceling the common interest-rate denominator reduces the equality to a quadratic in the five-year discount factor; the admissible root gives i = 10.76%, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the quadratic in the five-year discount factor; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the quadratic in the five-year discount factor; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the quadratic in the five-year discount factor; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the quadratic in the five-year discount factor; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: compare two scholarship streams
At 10% effective annually, Scholarship A pays 300 at each year-end for five years. Scholarship B pays 200 at years 1 and 2, then 200 every year from year 6 onward. How much greater is the present value of B than the present value of A?
A 351.71
B 401.71
C 451.71
D 501.71
E 551.71
Variant answer in brief
The two present values are 1,137.24 and 1,588.95, so B exceeds A by 451.71, choice C.
Setup
Setup
Value the finite scholarship and the split stream separately at the common valuation date.
PA=300a5∣0.10=1137.2360
Model
Model
The later perpetuity has its value one period before its first payment, so discount that value five years.
PB=200a2∣0.10+200v5a∞∣0.10=1588.9501
Compute
Compute
Subtracting the five-payment annuity value from the split-stream value gives 451.7141.
PB−PA=1588.9501−1137.2360=451.7141
Answer
Answer
Scholarship B is worth 451.71 more at time zero, corresponding to choice C.
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