The Society of Actuaries (SoA) kindly produces a bank of sample questions for their Financial Mathematics exam.

These sample questions are designed to be typical of the type and format of questions to be set on any SoA Financial Mathematics exam.

So, if you intend to take the SoA FM Financial Mathematics exam, it seems only sensible to practice working these sample exam questions.

What could go wrong?

Plenty, as it turns out.

Here is Question 1 from the SoA 2017 FM sample questions:

The first thing you had better notice is that there are some terms you need to be able to recognize and whose meaning you need to bring to mind rapidly and easily:

- Annual nominal rate of interest
- Convertible semiannually
- Annual force of interest

If you cannot readily recall the meaning of these terms, with reference to worked examples, from a mental image – a pattern of thought – then you are up the proverbial creek without a paddle.

Even if you can recall each of these ideas you still have to relate them to a formula – which is just a way of stating, in an algebraic expression, what the question is telling us.

So let’s imagine you are studying cold and you begin with question 1.

Is your brain overloaded?

Is the mix of concepts and formulas to recall causing you to stress out?

What do you do?

You have essentially two choices:

- Go for rote memorization of the formulas. Practice them over and over until they are sticking in your mind.
- Dig into what the basic concepts are for insight until the formulas become obvious to you.

You have come to a fork in the road, and it’s up to you which path you take –

The rote memorization path seems attractive: it’s more or less an easier path and just requires time to keep the formulas in the front of your mind.

The insight path seems harder: it’s mentally harder to dig into the meaning of concepts and formulas and it seems slow going.

Yet … formulas that are rote learned are easily, and quickly, forgotten. What’s more, if a question on the FM exam is worded somewhat differently from what you have seen before, you probably will not know which formula, or which version of a formula, to use.

When you have insight into where the formula comes from, why it’s the way it is, and how it’s used, you have set up a pattern of thought that is both easily recalled and is also very flexible.

The Society of Actuaries answer for this question depends on a few basic insights:

The SoA answer assumes you are familiar with how compound interest accumulates both in fixed periods per year, and continuously. We will discuss the conceptual basis of these in future posts.

For now, remember: choose the insights fork in the road every time. It’s a more stable, more permanent, road.

Of course practice sample exam questions: use them to build and to test your basic understanding and insights, and feel how progressively stronger and more capable you become in answering financial mathematics questions.

Most important: __study as many worked examples as you can__, because these help you build appropriate patterns of thought, which helps reduce your memory load and thinking load when you are attempting an exam question.

Here are a couple of samples of what we mean by worked examples that help you build long-lasting, more easily remembered, patterns of thought in your mind:

Gary Davis is a mathematics educator and mathematician with a Ph.D. in Mathematics from Monash University, Australia. He was instrumental in establishing the Data Science program at the University of Massachusetts Dartmouth and has periodically run a course in Financial Mathematics He has been the Boeing Distinguished Professor of Mathematics Education at Washington State University, Visiting Professor of Mathematics Education at Rutgers University in New Jersey, Visiting Professor in the Mathematics Education Research Centre, University of Warwick, UK, Professor of Education at the University of Southampton, UK, and Director of the Institute for Mathematics Education, LaTrobe University, Melbourne, Australia.

Gary lives in Massachusetts, USA, with wife Linda, dog Daisy and cat Bella.