Worked solution · Exam FM
This Exam FM sample reference tests Loan Balances and Amortization. A 20-year lump sum produces interest 1.65330X. Ten level payments produce total interest 0.29505X. Their difference equals 1,000, giving X = 736.24 and choice D.
Independent solution
Setup
Express total interest under the 20-year lump-sum repayment.
Model
For ten level payments, total interest is total payments minus principal.
Compute
Set the lump-sum interest 1,000 above the level-payment interest and solve X = 736.2404.
Answer
The borrowed amount is approximately 736, selecting choice D.
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 2,000 loan charges 6% annually. Compare repayment by one lump sum at year 15 with repayment by eight level annual payments beginning at year 1. Calculate how much more total interest the lump-sum method produces.
The lump-sum interest is 2,793.12, while eight level payments produce 576.58 of interest. The difference is 2,216.54, choice D.
Setup
Compute maturity interest under the single-payment method.
Model
Compute the eight-year level payment and subtract principal from total payments.
Compute
The two interest totals are 2793.12 and 576.58, differing by 2216.54.
Answer
Deferring repayment creates 2,216.54 more interest, selecting choice D.
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Drill the method: Exam FM Loan Amortization and Balances problems
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