Worked solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. After payment 40, twenty payments remain. Payment 41 equals 1,000 times 0.98 to the fortieth, and the remaining declining annuity discounted at 0.75% monthly is worth 6889.11, so choice A is correct.
Independent solution
Setup
The monthly rate is 9% divided by 12, and the first remaining payment is the original payment reduced forty times.
Model
The balance immediately after payment 40 is the present value of payments 41 through 60.
Compute
Evaluating the finite geometric present value gives 6889.114798.
Answer
The outstanding balance is approximately 6,889, selecting choice A.
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 48-payment monthly loan has payments that decline 1% each month and charges 6% nominal interest convertible monthly. Immediately after payment 24, the balance is 3,000. Calculate the first payment.
Payments 25 through 48 are the original payment times successive powers beginning with 0.99 to the twenty-fourth. Their unit present-value factor at 0.5% monthly gives first payment 189.05, choice B.
Setup
Express every remaining payment in terms of the unknown first payment P.
Model
Value the 24 remaining payments immediately after payment 24.
Compute
Solving the finite geometric equation gives P = 189.05.
Answer
The original first payment is 189.05, selecting choice B.
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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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