Worked solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. At the beginning of year 7, six payments have been made. Accumulating the original loan for six years and subtracting the accumulated value of those payments gives balance 3659.90, so choice B is correct.
Independent solution
Setup
The requested date is immediately after the sixth year-end payment.
Model
Use the retrospective balance: accumulated principal minus the accumulated value of payments already made.
Compute
The accumulated principal is 5360.38 and the six payments accumulate to 1700.48, leaving 3659.90.
Answer
The outstanding balance is approximately 3,660, which is choice B.
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 loan charges 6% annual effective interest. After five end-of-year payments of 600, its balance immediately after payment 5 is 4,200. Calculate the original loan principal.
At year 5, accumulated principal equals the 4,200 remaining balance plus the accumulated value of five payments. Discounting that total gives original principal 5,665.90, choice A.
Setup
Write the retrospective balance at time 5 with the original principal as the unknown.
Model
Move the accumulated payments to the balance side and discount five years.
Compute
The resulting original principal is 5665.90.
Answer
The original loan was 5,665.90, which is choice A.
Calculator reproduction
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Drill the method: Exam FM Loan Amortization and Balances problems
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