Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. The monthly payments form twice an increasing annuity-immediate for 60 months at 1% per month; its present value is 2,474.60, choice C.
Independent solution
Setup
The payment in month k is 2k, and the quoted nominal rate gives a monthly effective rate of one percent.
Model
Factoring out two leaves the standard 60-payment increasing annuity-immediate.
Compute
Evaluating its closed form gives 1,237.30; restoring the factor two gives 2,474.60.
Answer
The annuity purchase price is therefore about 2,475, which is choice C.
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30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.
Original practice · fully worked
A mural cooperative pays an artist 5 at month 1, 10 at month 2, and continues increasing each monthly installment by 5 through month 12. Money is valued at 0.5% per month. Determine the contract's present value.
Five times the 12-payment increasing-annuity value is 374.16, choice C.
Setup
Month k carries payment 5k, so the contract is a scaled finite increasing annuity.
Model
Discount each installment by k months at the monthly rate rather than using an annual factor.
Compute
The 12-term time-weighted discount sum multiplied by five equals 374.16265.
Answer
Thus the contract is worth 374.16 today, which is choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities problems
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