This Exam FM sample reference tests Annuities and Perpetuities. At semiannual rate j, the perpetuity value reduces to 300 + 300/j + 200/j² = 475,000; the positive root is j = 2.084%, equivalent to 4.21% annually, choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the level-plus-increasing perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the level-plus-increasing perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the level-plus-increasing perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the level-plus-increasing perpetuity decomposition; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: perpetual cooperative patronage payments
A farm cooperative pays 100 immediately and 100 six months later. Starting one year from now, payments are 150, 200, 250, and so on forever at six-month intervals. At 3% per half-year, calculate the present value.
A 50,000.00
B 55,555.56
C 58,988.89
D 60,500.00
E 65,000.00
Variant answer in brief
Separating the delayed level and increasing components gives 58,988.89, choice C.
Setup
Setup
The first two payments are valued separately because the arithmetic pattern begins only at the third payment.
v=1/1.03
Model
Model
From year one onward, split the stream into a level 150 perpetuity and a 50-per-period increasing component.
PV=100+100v+v2(1−v150+(1−v)250v)
Compute
Compute
Discounting that combined perpetuity by two half-years and adding the first two payments gives 58,988.8889.
PV=58988.8889
Answer
Answer
The present value is 58,988.89, so choice C is correct.
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.
