This Exam FM sample reference tests Annuities and Perpetuities. The perpetual income is worth 975.61; the six beginning-of-year investments have present-value factor 5.3295, so X = 183.06, choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B is inconsistent with the six-term growing-investment present-value series; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the six-term growing-investment present-value series; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the six-term growing-investment present-value series; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the six-term growing-investment present-value series; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: break-even seed funding for a repair café
A repair café invests X now and at the beginnings of the next three years; each investment is 4% larger than the preceding one. It then earns 90 at every year-end forever, starting in year 1. At 8% effective, what X gives zero net present value?
A 250.00
B 275.00
C 297.37
D 320.00
E 350.00
Variant answer in brief
Perpetual income value 1,125 divided by the four-investment factor gives X = 297.37, choice C.
Setup
Setup
There are four investments at times zero through three and a perpetuity of income beginning at year one.
PVincome=90/0.08=1125
Model
Model
The cost present values decline geometrically by the ratio 1.04 divided by 1.08.
PVinvest=Xk=0∑3(1.04/1.08)k
Compute
Compute
Their factor is 3.78321394; dividing the income value 1,125 by it yields 297.3662.
X=3.783213941125=297.3662
Answer
Answer
The break-even initial amount is 297.37, 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.
