Worked solution · Exam FM
This Exam FM sample reference tests Arithmetic-Increasing Perpetuity with Multi-Year Spacing. Treat each three-year block as one period. Its effective rate is 19.1016%, and the increasing-perpetuity factor is 1/J plus 1/J squared. Solving the 655.56 price gives X = 20.083, choice C.
Independent solution
Setup
Convert the 6% annual yield to an effective rate per three-year payment interval.
Model
At three-year intervals the payments are X, 2X, 3X, and so on.
Compute
Use the arithmetic-perpetuity identity.
Answer
The first payment is approximately 20, choice C.
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Original practice · fully worked
A perpetuity pays 10 at year 3, 20 at year 6, 30 at year 9, and continues increasing by 10 every three years. Its present value is 300. Determine the annual effective yield.
The three-year rate solving 300 = 10(1/J + 1/J squared) is 20%. Converting that rate to an annual effective yield gives 6.2659%, choice C.
Setup
Let J be the effective yield over one three-year payment interval.
Model
Solve the positive quadratic root.
Compute
Convert the three-year rate to an annual effective yield.
Answer
The annual yield is 6.27%, choice C.
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