Worked solution · Exam FM
This Exam FM sample reference tests Rate Conversion in an Annuity. The conversion-period condition implies an annual accumulation factor of 1.0614 regardless of m. Solving a-angle-n at 6.14% equal to 5.5554 gives n = 7, choice A.
Independent solution
Setup
If j is the conversion-period rate and there are m periods per year, the annual effective accumulation is supplied directly.
Model
The annual payments are valued with the annual effective rate.
Compute
Solving the annuity equation gives a term essentially equal to seven years.
Answer
The annuity has seven payments, choice A.
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Original practice · fully worked
A nominal rate is convertible m times per year, with conversion-period rate j satisfying one plus j to the m equal to 1.08. Determine the present value of nine annual payments of 1 made at year-end.
The power condition gives an 8% annual effective rate. Nine year-end payments have present value a-angle-9 at 8%, equal to 6.2469, choice C.
Setup
The conversion condition is already the one-year accumulation factor.
Model
Use i = 8% for annual cash flows.
Compute
Evaluate the annuity-immediate factor.
Answer
The present value is 6.2469, choice C.
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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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