This Exam FM sample reference tests Discrete Crediting Date. The next common semiannual boundary is month 288, not month 285 or 286. Thus the discrete answer is 288 months. The result agrees with the published answer key, choice E.
How to solve this Discrete Crediting Date question
Setup
Setup
Write both accounts’ values after t years using their actual crediting periods: two credits per year for one account and twelve for the other.
1000(1.03)2t=2000(1.0025)12t
Model
Model
Solving the continuous equality gives t = 23.775 years, or 285.3 months. Equality is only realized when both accounts have reached an applicable crediting date.
t=2ln1.03−12ln1.0025ln2=23.775 years
Compute
Compute
The next common semiannual boundary is month 288, not month 285 or 286. Thus the discrete answer is 288 months.
12t=285.3,next semiannual credit date=288
Answer
Answer
The calculation gives 288 for discrete crediting date, matching published choice E.
n=288 months(E)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (276) does not match the checked discrete crediting date result (288); no distinct standard one-step error is identifiable.
BChoice B (282) does not match the checked discrete crediting date result (288); no distinct standard one-step error is identifiable.
CChoice C (285) does not match the checked discrete crediting date result (288); no distinct standard one-step error is identifiable.
DChoice D (286) does not match the checked discrete crediting date result (288); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: first common credit date after two accounts cross
Account A starts with 1,000 and earns 6% nominal interest convertible semiannually. Account B starts with 990 and earns 6.2% nominal interest convertible monthly. Values are compared only on dates when both accounts credit interest. Find the first comparison date, in months, when B is at least as large as A.
A 36 months
B 42 months
C 48 months
D 54 months
E 60 months
Variant answer in brief
The continuous crossing is at 3.691 years; the next common credit date is 48 months. The first qualifying comparison date is 48 months, which is choice C.
Setup
Setup
Convert each nominal quote to its annual accumulation factor and solve the value equality in continuous time.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
