This Exam FM sample reference tests Annuities and Perpetuities. At force 0.06, the 20-year increasing annuity-due factor is 102.614, so X = 5,847.155; applying the 25-year factor to the same X gives about 779,336, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the two increasing annuity-due discounted sums under force 0.06; no distinct standard single-step error producing it is identifiable.
BChoice B is inconsistent with the two increasing annuity-due discounted sums under force 0.06; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the two increasing annuity-due discounted sums under force 0.06; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the two increasing annuity-due discounted sums under force 0.06; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: first grant in an increasing cultural-fund schedule
A cultural fund pays X immediately, 2X one year later, and continues increasing by X annually through the tenth payment. At 5% effective annually, the stream is worth 10,000. Determine X.
A 200.00
B 225.00
C 241.88
D 260.00
E 280.00
Variant answer in brief
The ten-payment increasing annuity-due factor is 41.34247, so X = 241.88, choice C.
Setup
Setup
Payment k equals kX and occurs at time k minus one because the first grant is immediate.
10000=Xk=1∑10kvk−1,v=1/1.05
Model
Model
Factor out X and evaluate the ten-term time-indexed discount sum.
k=1∑10kvk−1=41.3424719
Compute
Compute
That factor is 41.3424719, making the base payment 241.8820.
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.
