Worked solution · Exam FM
This Exam FM sample reference tests Equation of Value under a Constant Force. Using time 20 as the comparison date, the deposits occur at times n/2 for n from 1 through 40. Discounting both sides back twenty years yields the expression in choice E.
Independent solution
Setup
Index the forty deposits by n, with deposit n occurring at time n divided by two.
Model
Write the balance at time 20 by accumulating each deposit under force 4.5%.
Compute
Multiply the equation by the twenty-year discount factor.
Answer
This index range and sign pattern are exactly those of choice E.
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Error diagnosis
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Original practice · fully worked
A savings plan receives 300 at each quarter-end for eight years. The account earns a constant annual force of 3%. Find the balance immediately after the final deposit.
Accumulating each of the thirty-two quarterly deposits to time 8 under the 3% force gives 10809.33, choice D.
Setup
Deposit k occurs at time k divided by four, for k from 1 through 32.
Model
Accumulate every payment to the final date.
Compute
The finite exponential sum evaluates directly.
Answer
The terminal balance is 10809.33, choice D.
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.
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