This Exam FM sample reference tests Arithmetically Increasing Annuities. Equating the accumulated increasing deposits to the perpetuity price reduces to an annuity-due factor of 20. This gives i = 12.304% and a perpetuity price of 81.27, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A uses a rate above the root of the annuity-due equation, which understates the perpetuity price.
BChoice B treats the increasing deposits as a level annuity with average payment 5.5.
CChoice C shifts the deposit sequence by one year and loses one period of accumulation.
EChoice E uses a rate below 12.304%, inconsistent with the required annuity-due factor of 20.
Original practice · fully worked
Original variant: perpetuity payment funded by a stepped reserve
A reserve receives year-end deposits of 2, 4, 6, and so on through 20 in year ten. The account earns 8% annually. Immediately after the final deposit, the balance buys a perpetuity-immediate at the same rate. Determine the perpetuity's annual payment.
A 8.92
B 10.14
C 11.29
D 12.48
E 14.11
Variant answer in brief
The stepped deposits accumulate to 141.1372; multiplying the perpetuity price by 8% gives an annual payment of 11.2910, choice C.
Setup
Setup
Accumulate each even-numbered deposit to time 10 at 8%.
F10=t=1∑102t(1.08)10−t
Model
Model
A perpetuity-immediate paying X has price X divided by 0.08, so X equals 8% of the available fund.
X=0.08F10
Compute
Compute
The deposit accumulation is 141.1372, giving X = 11.2910.
F10=141.1372
X=11.2910
Answer
Answer
The annual perpetuity payment is approximately 11.29, 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.
