This Exam FM sample reference tests Annuities and Perpetuities. Keep the ten deposits as principal and accumulate each annual simple-interest transfer at 8%; the total factor is 18.4683, giving X = 541.47, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A is inconsistent with the principal-plus-transferred-interest accumulation; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the principal-plus-transferred-interest accumulation; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the principal-plus-transferred-interest accumulation; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the principal-plus-transferred-interest accumulation; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: museum reserve with transferred interest
A museum places X into a noncompounding reserve at the beginning of each of six years. At each year-end, the reserve pays 10% simple interest on all principal then present into a separate account earning 6% annually. Find X if the two accounts together must hold 10,000 at the end of year 6.
A 1,081.33
B 1,141.74
C 1,201.48
D 1,261.22
E 1,321.06
Variant answer in brief
Principal and accumulated transfers provide a factor of 8.323063, so X = 1,201.48, choice C.
Setup
Setup
Track the reserve principal separately from the account that receives its annual interest.
V6=6X+k=1∑6(0.10kX)(1.06)6−k
Model
Model
At year k, reserve principal is kX, so the transfer is 0.10kX and grows for six minus k years.
V6=8.32306275X
Compute
Compute
The six principal deposits plus accumulated transfers produce 8.32306275X at year 6.
X=8.3230627510000=1201.4808
Answer
Answer
A deposit of 1,201.48 at each year-beginning meets the target, 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.
