Worked solution · Exam FM
This Exam FM sample reference tests Deposits Accumulated into a Semiannual Perpetuity. Accumulating the five beginning-year deposits to year 10 gives 1703.81. The half-year rate equivalent to 12% annually is 5.8301%, so the perpetuity-immediate payment is 99.33, choice A.
Independent solution
Setup
Place the beginning-year deposits at times zero through four and accumulate each to time 10.
Model
The accumulated fund is 1703.8111.
Compute
Convert the annual effective yield to a half-year effective rate and price a perpetuity-immediate.
Answer
The semiannual payment is approximately 99, choice A.
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Original practice · fully worked
Deposits of 100q, 150q, and 200q are made at times 0, 1, and 2 into a fund earning 8% annually. At time 6 the fund buys a perpetuity-immediate paying 120 every half-year, valued at a 10% annual effective yield. Determine q.
The perpetuity requires 2458.57 at time 6, while the unscaled deposits accumulate to 651.18. Their ratio is q = 3.7755, choice C.
Setup
Find the half-year rate and the fund required for the perpetuity.
Model
Accumulate one unit of the stated deposit pattern to time 6.
Compute
The actual accumulated deposits equal q times this base value.
Answer
The deposit scale is 3.78, choice C.
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