This Exam FM sample reference tests Geometric Perpetuity Due. Convert the quarterly discount factor to an annual effective rate: vq to the power −4 minus 1 equals 0.10601, or 10.6%. The result agrees with the published answer key, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (10.0%) does not match the checked geometric perpetuity due result (10.6%); no distinct standard one-step error is identifiable.
BChoice B (10.2%) does not match the checked geometric perpetuity due result (10.6%); no distinct standard one-step error is identifiable.
CChoice C (10.4%) does not match the checked geometric perpetuity due result (10.6%); no distinct standard one-step error is identifiable.
EChoice E (10.8%) does not match the checked geometric perpetuity due result (10.6%); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: present value of a growing perpetuity-due
An endowment pays 200 immediately. Every later annual payment is 2% larger than the preceding payment, and payments continue forever. At a 7% annual effective rate, calculate the present value.
A 4,000
B 4,080
C 4,280
D 4,366
E 5,000
Variant answer in brief
Summing the perpetuity-due gives 4280. The endowment value is 4,280, selecting choice C.
Setup
Setup
Because the first payment is immediate, index the geometric present-value series from time 0.
CFt=200(1.02)t,t=0,1,2,…
Model
Model
Each successive present-value term is multiplied by 1.02/1.07, which is less than one.
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.
