Worked solution · Exam FM
This Exam FM sample reference tests Annuities and Perpetuities. Decompose the decreasing series into a level annuity and an arithmetic decrement; solving the value equation gives the first payment 705.36, choice C.
Independent solution
Setup
Write payment t as the unknown first payment minus five for each elapsed payment interval.
Model
Discount the level portion and the arithmetic decrement on the same year-end schedule.
Compute
The level-annuity factor is 15.37245 and the decrement adjustment is 843.11275.
Answer
The first payment is approximately 705.36, so the listed answer 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 maintenance contract is worth 5,000 today and makes 20 year-end reimbursements. The first is X, and each later reimbursement is 10 less than the preceding one. At 4% effective annually, determine X.
Discounting the level first-payment component and the ten-unit decrements gives X = 450, choice C.
Setup
Express every reimbursement from its payment index and discount it to contract issue.
Model
The level portion contributes 13.5903263X while the sequence of decrements removes 1,115.6469.
Compute
Solving the resulting linear equation gives an exact first payment of 450.
Answer
The first reimbursement is 450.00, corresponding to 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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