Worked solution · Exam FM
This Exam FM sample reference tests Arithmetic Annuity-Due. Pairing equal adjacent payments gives a 42-term two-month arithmetic series multiplied by one plus the monthly discount factor. Its present value is 14062.03, choice D.
Independent solution
Setup
The monthly effective rate is 0.4%, and payments at months 2k and 2k plus 1 both equal 100 plus 5k.
Model
Factor each adjacent pair and sum over k from zero through 41.
Compute
Evaluate the finite level and arithmetic components of the two-month series.
Answer
The present value rounds to 14062, choice D.
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Error diagnosis
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Original practice · fully worked
An annuity-due makes 24 quarterly payments. Payment k, numbered from zero, is P plus 10k. Interest is a nominal annual rate of 6% compounded monthly. The annuity's present value is 6,000. Determine P.
The equivalent quarterly rate is 1.5075125%. Separating the level and gradient present values and solving the linear equation gives P = 187.51, choice C.
Setup
Convert three monthly compounding periods into one quarterly effective rate.
Model
Separate the unknown level payment from the known increase by quarter.
Compute
The due factor is 20.314637 and the gradient sum is 219.084828.
Answer
The first payment is 187.51, choice C.
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