This Exam FM sample reference tests Geometric Annuity Exchange. Equating 25X/1.08 to 1,250 gives X = 54. This cancellation is specific to equal growth and yield rates. The result agrees with the published answer key, choice A.
How to solve this Geometric Annuity Exchange question
Setup
Setup
At time 5, the original perpetuity is worth 100/0.08 = 1,250. Move the replacement stream to that same date before comparing it.
V5=100/0.08=1250
Model
Model
Each replacement payment grows at the same 8% rate used for discounting. Consequently every discounted term has the same time-5 value X/1.08, and the 25-term sum is 25X/1.08.
1250=Xt=1∑251.08t−1vt
Compute
Compute
Equating 25X/1.08 to 1,250 gives X = 54. This cancellation is specific to equal growth and yield rates.
1250=X(25/1.08)⟹X=54
Answer
Answer
The calculation gives 54 for geometric annuity exchange, matching published choice A.
X=54(A)
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