Worked solution · Exam FM
This Exam FM sample reference tests Annuities. The first 20 growing payments have present value 157337.48. The perpetuity beginning with payment 21 contributes 49202.44, giving total 206539.93 and choice C.
Independent solution
Setup
Split the payment stream after payment 20 because the growth rate changes at payment 21.
Model
Value the finite 4%-growth segment directly and value the later 1%-growth perpetuity at time 20.
Compute
The finite segment is 157337.48 and the discounted tail is 49202.44, totaling 206539.93.
Answer
The perpetuity price is approximately 206,540, so choice C is correct.
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Original practice · fully worked
A perpetuity pays 2,000 at year 1. Payments grow 2% annually through payment 10. Beginning with payment 11 they grow at a constant rate g forever. At a 7% annual yield, the price is 35666.33. Calculate g.
The first ten payments contribute 15213.00. Removing that value and bringing the residual to time 10 identifies the growing-perpetuity denominator, giving g = 1.00%, choice D.
Setup
Value the first ten payments using their known 2% growth pattern.
Model
The residual price is the time-0 value of a perpetuity whose first tail payment is the year-10 payment grown once at g.
Compute
Using the quoted price and the first-segment value 15213.00, solving the tail equation gives g = 1.0000%.
Answer
The long-run growth rate is 1.00%, which is choice D.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities problems
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