The Force of Interest Example (Actuarial Exam FM–Financial Mathematics–Module 1, Section 8, P1)

In this Exam FM example, we compare two accounts that credit interest differently:
Account A uses a simple discount rate.
Account B uses an interest rate compounded semiannually.
You're told that after two years, the forces of interest for both accounts are equal — and your task is to determine the nominal rate for Account B. This video walks you through the logic, common traps (like misinterpreting symbols), and how to convert between discount, effective, nominal, and force of interest rates.

Perfect for students preparing for Actuarial Exam FM / Financial Mathematics and for anyone needing a deeper understanding of interest theory concepts used on the exam.

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SOA Exam FM (Financial Mathematics) Module 1, Section 8

After completing this video you should be able to:
Define and recognize the definitions of the following terms: the force of interest.
Given any one of the effective interest rate, the effective discount rate, or the force of interest, calculate any of the other items.

Example used in the video:
Account A credits interest using a 10% simple discount rate. Account B uses an interest rate of 𝑖, compounded semiannually. At the end of two years, the forces of interest for Accounts A and B are equal.

Determine 𝑖.

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