Worked solution · Exam FM
This Exam FM sample reference tests Loan Amortization. For a level-payment loan, principal portions grow by one plus the monthly rate; over 24 months the factor is (1.10)², so the 30th principal portion is 500(1.10)² = 605, choice C.
Independent solution
Setup
In a level-payment amortization, the interest decline from one month to the next becomes an equal increase in principal repaid.
Model
Thus successive principal portions grow at the monthly interest factor.
Compute
Payments six and thirty are 24 months apart, or two annual effective periods, giving growth factor 1.10 squared.
Answer
The later principal portion is 605, which is 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 gallery mortgage has level monthly payments. The principal portions of payments 10 and 34 are 300 and 376.32, respectively. Determine the annual effective interest rate.
Principal grows by 1.2544 over two years, so the annual effective factor is its square root, giving 12%, choice C.
Setup
Successive principal portions in a level-payment schedule grow at the monthly loan factor.
Model
The two observed portions are 24 months, or two annual effective periods, apart.
Compute
Their ratio is 1.2544, whose two-year annual-factor root is 1.12.
Answer
The annual effective interest rate is 12.00%, corresponding to 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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