Worked solution · Exam FM
This Exam FM sample reference tests Monthly Perpetuity with Annual Step Growth. The first twelve monthly payments are worth 5756.43 at the exact monthly rate. Treating each twelve-payment block as an annual unit growing 5% while discounting 8% gives total value 207231.44, choice D.
Independent solution
Setup
Convert the annual effective yield to its equivalent monthly rate and price the first twelve-payment block.
Model
Each later block is one year farther away and 5% larger.
Compute
Evaluate the geometric block series.
Answer
The perpetuity value is approximately 207231, choice D.
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Original practice · fully worked
A monthly perpetuity pays 400 for the first twelve months. At the start of each later twelve-payment block, the monthly amount increases by annual rate g. Its present value is 100,000 at a 6% annual effective yield. Determine g.
The first monthly block is worth 4651.52. Solving the geometric block-price equation gives annual step growth 1.0694%, choice C.
Setup
Price the first twelve payments at the exact monthly equivalent of 6%.
Model
Successive block values form a geometric series with ratio one plus g divided by 1.06.
Compute
Rearrange for the annual step growth.
Answer
The block growth rate is 1.07%, choice C.
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