Exam FM practice problems: Interest rates and the time value of money

10 problems · Untimed · Worked solution after each answer

Simple and compound interest, nominal and effective rates of interest and discount, the force of interest, inflation and equations of value. This drill covers topic 1 of the Exam FM syllabus, Time Value of Money (5–15% of the exam).

1a Interest and discount definitions
1b Simple and compound interest and variable force
1c Equivalent rates of interest and discount
1d Equations of value

Line drawing of coin stacks growing taller with a sprout on the tallest, beside an hourglass and a piggy bank

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: Interest rates and the time value of money

Convert every rate to one effective rate per payment period before you do anything else: (1 + i⁽ᵐ⁾/m)ᵐ = 1 + i = (1 − d)⁻¹ = e^δ.
With a varying force of interest, the accumulation factor from s to t is exp(∫ from s to t of δ(r) dr).
Simple interest grows linearly, compound interest geometrically; at times under one period simple interest is larger.
The real rate of interest is (1 + i)/(1 + r) − 1, not i − r.

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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).