Exam FM practice problems: Loans and amortization

10 problems · Untimed · Worked solution after each answer

Amortization schedules, outstanding balances, the interest and principal in a payment, drop and balloon payments, and refinancing. This drill covers topic 3 of the Exam FM syllabus, Loans (15–25% of the exam).

3a Loan definitions
3b Loan balances, interest and principal, and refinancing

Line drawing of a small house with a key, a signed document and a calculator

Before you start

Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Loans and amortization

The balance just after payment k is the present value of the remaining payments (prospective) or the accumulated loan minus the accumulated payments (retrospective).
For a level-payment loan, the principal in payment k is P·v^(n − k + 1) and the interest is P·(1 − v^(n − k + 1)).
A drop payment is smaller than the regular payment and made one period after the last full payment; a balloon payment is larger and made with the last regular payment.
Refinancing replaces the old balance with a new loan: find the balance first, then solve the new loan.

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Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).