Worked solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. The 3% level-payment option totals 1344.31. Under constant principal, interest is i times the sum of balances 1,000 through 50, totaling 10500. Equating totals gives i = 3.28%, choice C.
Independent solution
Setup
Compute the level annual payment and its total over 20 years.
Model
The second option repays 50 principal each year, so total interest is i times the arithmetic sequence of opening balances.
Compute
Equating T1 = 1344.3142 to T2 gives i = 3.279182%.
Answer
The constant-principal option uses an annual rate of approximately 3.28%, selecting choice C.
Test the method on unseen problems
30 original loans problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A 12,000 loan can be repaid over ten years either by level annual payments at 4% or by 1,200 principal each year plus 5% interest on the opening balance. Calculate how much larger the total payments are under the constant-principal option.
The 4% level-payment schedule totals 14,794.91. Principal plus 5% interest on the ten opening balances totals 15,300.00, an excess of 505.09, choice E.
Setup
Compute the annual level payment and ten-payment total under option A.
Model
Under option B, add 12,000 principal to 5% of the ten opening balances.
Compute
The totals are 14794.91 and 15300.00, so the excess is 505.09.
Answer
The constant-principal option costs 505.09 more, selecting choice E.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 82 Exam FM loans practice problems.
Drill the method: Exam FM Loan Amortization and Balances problems
Keep studying
Work through the related free solutions for this topic, review the formulas you used, or keep every current Exam FM solution in one searchable PDF.
