Worked solution · Exam FM
This Exam FM sample reference tests Annuities. Payment k is 100 times 0.9 to the k−1 and earns 3% from its receipt date through year 20. Accumulating all twenty payments gives 1295.80, so the balance is 1,296 and choice D.
Independent solution
Setup
Write the declining payment and its accumulation time to the final receipt date.
Model
Recognize the terminal-value expression as a finite geometric sum.
Compute
Evaluating the twenty accumulated contributions gives 1295.795831.
Answer
The savings balance is approximately 1,296, selecting choice D.
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Original practice · fully worked
A saver makes twelve year-end deposits. The first is P and every later deposit is 5% smaller. The account earns 4% annually. Immediately after the twelfth deposit, the fund must equal 10,000. Calculate P.
Accumulating twelve unit-scaled deposits under 5% decline and 4% account growth gives factor 11.785246. Dividing 10,000 by this factor gives first deposit 848.52, choice E.
Setup
Express deposit k and its accumulation to the time-12 target.
Model
Factor out the unknown first deposit from the finite geometric sum.
Compute
The unit accumulation factor is 11.78524590, so P = 848.52.
Answer
The first deposit is 848.52, selecting choice E.
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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