This Exam FM sample reference tests Loan Rate from Principal Portions. Therefore X = 3,600/0.075 = 48,000. The result agrees with the published answer key, choice D.
How to solve this Loan Rate from Principal Portions question
Setup
Setup
For a level-payment loan, principal portions increase geometrically. Use the ten-period principal difference and the principal amount five periods later to identify v.
P(1−v10)=3600,Pv5=4871
Model
Model
The two relations give v⁵ = 0.69656 and hence i = 7.5%. The amount 3,600 equals one interest-rate multiple of the requested loan quantity X.
v5=0.69656,i=0.075
Compute
Compute
Therefore X = 3,600/0.075 = 48,000.
X=3600/i=48000
Answer
Answer
The calculation gives 48,000 for loan rate from principal portions, matching published choice D.
X=48000(D)
Continue without hunting through PDFs
All 461 Exam FM sample solutions in syllabus order
The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (44,000) does not match the checked loan rate from principal portions result (48,000); no distinct standard one-step error is identifiable.
BChoice B (45,250) does not match the checked loan rate from principal portions result (48,000); no distinct standard one-step error is identifiable.
CChoice C (46,500) does not match the checked loan rate from principal portions result (48,000); no distinct standard one-step error is identifiable.
EChoice E (50,000) does not match the checked loan rate from principal portions result (48,000); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: loan principal from two principal portions
An eight-payment level loan has principal portions 900 in payment 2 and 1,093.50 in payment 6. Principal portions grow geometrically with the loan rate. Calculate the original loan principal.
A 7,200.00
B 7,534.18
C 7,943.76
D 8,182.60
E 8,548.22
Variant answer in brief
The rate is 4.99%, first principal is 857.23, and the geometric principal sum is 8182.60. The original loan is 8,182.60, which is choice D.
Setup
Setup
Use the four-payment gap between the two principal portions to recover the loan rate.
900(1+i)4=1093.50⟹i=0.04989065
Model
Model
Back up one period to obtain principal in payment 1, then sum all eight principal portions because their total equals original principal.
P1=900/(1+i)=857.232129
Compute
Compute
The rate is 4.99%, first principal is 857.23, and the geometric principal sum is 8182.60.
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.
