This Exam FM sample reference tests Growing Monthly Retirement Annuity. The stream is worth 374,444. Compared with 374,500, it is short by 56, so the signed difference shown is −56. The result agrees with the published answer key, choice D.
How to solve this Growing Monthly Retirement Annuity question
Setup
Setup
Accumulate the twelve monthly deposits within the first year to obtain the first year-end amount. Annual blocks then grow by 2%, while discounting uses the monthly rate 0.5%.
j=0.06/12,A1=2000s12∣j=24671.12
Model
Model
Value the twenty-five annual blocks at time 0 as a geometric series with growth 1.02 and annual discount factor 1.005 to the power −12.
P=24671.12k=1∑251.02k−1(1.005)−12k
Compute
Compute
The stream is worth 374,444. Compared with 374,500, it is short by 56, so the signed difference shown is −56.
P=374444,374500−P=56
Answer
Answer
The calculation gives the statement identified by the conditions above for growing monthly retirement annuity, matching published choice D.
P=374444(D)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A does not satisfy the checked growing monthly retirement annuity conditions that select published choice D; no distinct standard one-step error is identifiable.
BChoice B does not satisfy the checked growing monthly retirement annuity conditions that select published choice D; no distinct standard one-step error is identifiable.
CChoice C does not satisfy the checked growing monthly retirement annuity conditions that select published choice D; no distinct standard one-step error is identifiable.
EChoice E does not satisfy the checked growing monthly retirement annuity conditions that select published choice D; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: monthly retirement stream with steady payment growth
A retirement contract pays 1,000 one month from now. Each subsequent monthly payment is 0.2% larger, for a total of 60 payments. At a nominal annual discount rate of 6% convertible monthly, calculate the present value.
A 50,882.14
B 52,791.36
C 54,735.12
D 56,482.20
E 60,000.00
Variant answer in brief
Evaluating the finite series gives present value 54735.12. The contract value is 54,735.12, which selects choice C.
Setup
Setup
Use a monthly discount rate of 0.5%; payment growth is 0.2% per month.
j=0.06/12=0.005,q=1.002/1.005
Model
Model
The discounted payments form a sixty-term geometric series with first term 1,000/1.005 and ratio 1.002/1.005.
PV=1.00510001−q1−q60
Compute
Compute
Evaluating the finite series gives present value 54735.12.
PV=54735.116906
Answer
Answer
The contract value is 54,735.12, which selects 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.
