This Exam FM sample reference tests Loan Amortization. Using quarters as the time unit, the six 800 advances occur at odd quarter indices, the 4,000 balance is at quarter 12, and 36 midmonth payments occur at n−0.5 thirds of a quarter; only choice E places every term correctly.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThis option mixes quarterly and monthly rate divisors while leaving payment exponents on incompatible scales.
BIts advance dates use the wrong month-to-quarter conversion.
CIt places the midmonth payments at integer quarter times rather than fractional positions.
DIt discounts at least one 4,000 balance to the wrong endpoint.
Original practice · fully worked
Original variant: monthly midperiod payments with later equipment draws
A studio owes 2,000 at month 0, borrows another 500 at months 3, 9, and 15, and pays X at the middle of each month for 18 months. The balance is zero at month 18. At 1% effective per month, determine X.
A 180.00
B 195.00
C 204.68
D 215.00
E 230.00
Variant answer in brief
Present-valuing the four advances and 18 half-month-shifted payments gives X = 204.68, choice C.
Setup
Setup
Month zero is the value date; later equipment draws are discounted by their exact month counts.
PVD=2000+500(v3+v9+v15)=3373.1397
Model
Model
A payment in month k occurs at k minus one-half, so the repayment annuity has a half-month timing shift.
PVP=Xk=1∑18vk−1/2=16.480056X
Compute
Compute
The advance value is 3,373.1397 and the payment factor is 16.480056.
X=3373.1397/16.480056=204.6801
Answer
Answer
Their quotient is a monthly payment of 204.68, corresponding to 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.
