When you deposit money in the bank, you normally receive money back over time based on the amount in your account. This is called interest and is shown as a percentage.

For example, imagine you put $100 in the bank, and they pay interest equal to 5% per year.

After one year, you will have your original $100, plus 5% of that amount = 0.05 x $100 = $5, for a total of $105.

If you leave this amount in the bank for another year, you will earn 5% on this new higher amount. So after two years you will have $105, plus 5% of $105 = $5.25, for a total of $110.25.

After three years, you will have $110.25 plus 5% of $110.25 = $5.51, for a total of $115.76.

Your money can grow faster and faster if you leave it in the bank to build interest.

How do actuaries use this?

Actuaries deal with costs that happen in the future. Understanding how money grows over time helps actuaries know how much they need to collect today in order to pay for these future costs.

For example, actuaries help design programs to provide income for seniors after they retire. Calculations like this help ensure that enough money is collected today to provide that income in the future. A good example of this is the Canada Pension Plan.

By doing so, actuaries have helped Canada maintain one of the lowest senior poverty rates in the world.

One word that we hear from time to time is “probability.” We hear it in weather reports; for example, we have a 30% probability of snow. It can also be used in other circumstances. For example, you could be playing basketball and estimate that you have 20% chance of making a shot.

If there is a 100% probability that something will happen, then it is certain to happen. On the other hand, if there is a 0% probability that something will happen, then it definitely will not happen. A 50% probability means that there is an equal chance that it will or will not happen.

In these examples, the probability is an estimate. However, there are times when probability can be exactly determined – like with cards. If you have a deck of 52 cards and you pull one card from that deck, what is the probability that the card is a heart?

We know that there are four suits in a deck – hearts, clubs, spades, and diamonds – and each suit has 13 cards – 2 to 10, and then Jack, Queen, King, and Ace. When you pull your card, there are 13 cards out of 52 that will be a heart. So the probability of pulling a heart can be calculated as 13 divided by 52, which is 25%.

You could also arrive at this number by considering that there are four suits in the deck, each with an equal number of cards, so your probability of pulling a heart is 1 divided by 4, which is also 25%.

How do actuaries use this?

Actuaries work with uncertain events; in other words, they don’t know whether or not these events will happen. In order to estimate how likely these events are, they need to estimate probabilities. Having a good understanding of how probability works is essential for actuarial work.

Homeowners can suffer damages to their houses due to severe weather events, often caused by climate change. Being able to estimate the probability of events such as hurricanes or floods allows insurance companies to design policies that can cover the cost of these damages and repair homes.

By doing so, actuaries help the public protect their homes from extreme weather and climate events.

16,000 people live in the town of Asgard, and 75% of them drive cars. We know that the town has equal numbers of men and women. We also know that 40% of the cars driven are blue, 35% are red, and 25% are green.

How do actuaries use this?

Auto insurance is available to drivers to cover the cost of damages caused by accidents. In order to properly price this insurance, they need to apply percentages to the population to determine how many drivers are in each category.

By doing so, actuaries help to ensure that individuals can have their cars repaired or replaced affordably if they get into an accident.

Citizens in a developing country are worried about losing their homes due to storms. Because they have a very low income, their homes are often made of weaker materials and they do not have the funds to purchase stronger ones or replace their homes if they are badly damaged.

In this country, there are 150,000 homes, and 500,000 people live in those homes. It costs $500 to replace a home that is lost in a storm. Looking at past years, it is expected that 1% of the homes will be lost in a given year.

How do actuaries use this?

Actuaries help design programs like this to assist families in developing countries who do not have the resources to rebuild if they lose their homes. By collecting an affordable amount from everyone – only $1.50 – they can have enough money on hand to help  everyone who has suffered a loss.

By doing so, actuaries can help improve living situations in countries where families have low income.

A group of your classmates’ parents are concerned about how they will be looked after when they retire. Some of them may need to live in long-term homes where they receive assistance with daily living.

The parents in this group are all 40 years old today. You expect that 80% of the group will live to be 85 years old, and that 10% of that group will need to live in a long-term care home. To pay for their care, you will need $40,000 per year for 5 years on average – you can put money in an investment fund where it will double every 15 years.

How do actuaries use this?:

Actuaries price insurance programs like this, letting individuals pay a small amount today, in order to cover a large cost that they may have in the future. Even though not everyone will need to live in a long-term care home, everyone benefits because they know that, if it happens, their costs will be covered.

By doing so, actuaries help look after Canada’s aging population.

A pharmaceutical company has recently developed a new drug that has proven to be very effective against certain types of cancer. However, the research that led to the drug was very expensive, and as a result the cost of the drug is $10,000 per month. Patients are required to take the drug for 2 years.

One country has a program that provides prescription drugs to its citizens, funded by an annual tax of $500 per person. The country would like to include this new drug in the program as well, but are concerned with how much they will need to raise their tax in order to pay for it. There are 5 million people in the country.

How do actuaries use this?:

Actuaries are involved in the design and pricing of health benefit plans and often need to estimate the cost of changes to coverage. As well, actuaries often have to deal with very large numbers, so any estimates need to be as accurate as possible.

By doing so, actuaries help make expensive medical treatments available to those that need them.