Worked solution · Exam FM
This Exam FM sample reference tests Growing Perpetuity-Due under a Force of Interest. A 12% force corresponds to an annual effective rate of 12.7497%. Pricing the first payment at time zero and the remaining growing stream gives 58829.14, so choice C is correct.
Independent solution
Setup
Convert the constant annual force to an annual effective yield.
Model
For a growing perpetuity-due, the time-zero payment advances the usual immediate formula by one period.
Compute
Substitute the effective yield and growth rate.
Answer
The purchase price rounds to 58829, choice C.
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Error diagnosis
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Original practice · fully worked
An endowment worth 30,000 funds a perpetuity-due whose first annual grant is 2,000 today. Valuation uses a constant annual force of 12%. If grants grow at rate g each year, determine g.
The force converts to 12.7497% effective. Solving the perpetuity-due price relation for growth gives g = 5.2330%, choice C.
Setup
Convert the force and write the due-perpetuity price equation.
Model
Rearrange to isolate the growth rate.
Compute
Insert the effective yield.
Answer
The grant growth rate is 5.23%, choice C.
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