This Exam FM sample reference tests Dated Deposits and Integer Timing. Therefore n is 11, not 12. The result agrees with the published answer key, choice A.
How to solve this Dated Deposits and Integer Timing question
Setup
Setup
Use the monthly rate 0.072/12 = 0.006 and express both deposits and the target value on the same date. The unknown n counts months.
j=0.072/12=0.006
Model
Model
Solving the equation of value as a real-number equation gives n = 11.73. The stated timing restriction requires the latest completed integer month that still satisfies the condition.
1700(1.006)−n+3400(1.006)−2n=6500(1.006)−60
Compute
Compute
Therefore n is 11, not 12.
n=11.73,nmax=11
Answer
Answer
The calculation gives 11 for dated deposits and integer timing, matching published choice A.
n=11(A)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B (12) does not match the checked dated deposits and integer timing result (11); no distinct standard one-step error is identifiable.
CChoice C (18) does not match the checked dated deposits and integer timing result (11); no distinct standard one-step error is identifiable.
DChoice D (24) does not match the checked dated deposits and integer timing result (11); no distinct standard one-step error is identifiable.
EChoice E (25) does not match the checked dated deposits and integer timing result (11); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: first integer anniversary at a target balance
A museum reserve deposits 5,000 at time 0 into an account earning 4% annually. Withdrawals may occur only on integer-year anniversaries. Find the first anniversary on which the account can fund a 7,000 withdrawal.
A Year 7
B Year 8
C Year 9
D Year 10
E Year 11
Variant answer in brief
The balance reaches 7,000 after 8.579 years, so the first permitted withdrawal date is anniversary 9. The first qualifying date is year 9, which is choice C.
Setup
Setup
Solve the accumulation inequality for a real-valued time before applying the anniversary restriction.
5000(1.04)t≥7000
Model
Model
Taking logarithms gives the exact crossing between years 8 and 9.
t≥ln(1.04)ln(1.4)=8.578942
Compute
Compute
The balance reaches 7,000 after 8.579 years, so the first permitted withdrawal date is anniversary 9.
n=⌈8.578942⌉=9
Answer
Answer
The first qualifying date is year 9, which is choice C.
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.
