Worked solution · Exam FM
This Exam FM sample reference tests Geometric Perpetuities. The mistaken first payment identifies the unchanged contract price as 1500 divided by 0.107. Using the correct denominator 0.098 gives a first payment of 1373.83, choice D.
Independent solution
Setup
Let P be the sale price and let r = -0.02 be the annual payment growth rate.
Model
The mistaken calculation used an 8.7% yield and first payment 1500, which determines the price the company intended to charge.
Compute
Keep that price fixed and replace the mistaken yield with 7.8%.
Answer
The corrected first payment rounds to 1374, choice D.
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Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A scholarship fund is priced at 5,000 and pays 250 one year from now. Subsequent annual payments grow at a constant rate g forever. The annual effective yield is 6%. Determine g.
The geometric-perpetuity equation gives 5000 = 250 divided by 0.06 minus g. Solving yields g = 1.0%, choice C.
Setup
The first scholarship payment is one year away, so use the perpetuity-immediate formula.
Model
Insert the quoted price, first payment, and yield.
Compute
Invert the equation and isolate the growth rate.
Answer
Annual payments grow by 1.0%, choice C.
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.
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