Worked solution · Exam FM
This Exam FM sample reference tests Annuities. At year 15, the first deposit has 14 years of 8% growth and each later deposit has one fewer. Summing the growing deposits produces factor 32.284034, so X = 61.95, choice C.
Independent solution
Setup
Deposit k has amount X times 1.03 to the k minus 1 and accumulates from year k to year 15.
Model
Factor out X from the finite geometric accumulation sum.
Compute
The accumulation factor is 32.28403395, giving X = 61.950127.
Answer
The first deposit is approximately 62, selecting choice C.
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Original practice · fully worked
A saver deposits 100 at year 1 and makes nine further year-end deposits, each growing by the same rate g. The account earns 6% annually. The fund immediately after the year-10 deposit is 1429.63. Calculate g.
Equating the ten accumulated deposits to the quoted year-10 fund and solving the geometric sum gives growth rate 2.00%, choice E.
Setup
Write deposit k and its accumulation to year 10.
Model
Set that finite sum equal to the quoted terminal fund.
Compute
The relevant root is g = 2.000000%.
Answer
The annual deposit growth rate is 2.00%, 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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