Worked solution · Exam FM
This Exam FM sample reference tests Loan Amortization. Valuing the first five payments at 11% and the last five at 12% deferred five years gives factor 5.83516; hence X = 20,000/5.83516 = 3,427.50, choice C.
Independent solution
Setup
Split the ten repayments at the interest-rate change after year five.
Model
The first block uses the 11% annuity factor; the second block uses 12% at its local date and is then discounted through the first five years at 11%.
Compute
The combined present-value factor is 5.83516, giving a payment of 3,427.50.
Answer
Therefore the annual payment is 3,427.50, 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 bakery borrows 12,000 and repays it with eight equal year-end payments. Interest is 5% effective for the first four years and 7% effective for the last four. Find the level payment.
The two four-payment blocks have combined value factor 6.33262, giving 1,894.95, choice C.
Setup
Partition the payments where the contractual rate changes.
Model
Value the later four-payment annuity at year four using 7%, then discount that value to the loan date through the 5% period.
Compute
Adding the early block gives a total factor of 6.3326176.
Answer
The level annual payment is 1,894.95, which is choice C.
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
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