Lesson 3

Lesson Topic: Simple and Compound Interest - What is it and how is it calculated?

Goal: To review the concept of simple interest and then expand that to include compound interest. Students will learn and practice the formula and then see how it is applied to real world investments.

Lesson Overview:

1. Class discussion – What do they remember about interest?

2. Lecture/Background info – What is Interest?

3. Video – Middle School Money Matters Video 7-5 : Basic Interest

4. Math lesson – review how to calculate simple interest, introduction to compound interest.

5. Student work – calculating interest earned and interest paid.

6. Wrap-up or Extension activity

Class Discussion Questions – What do they know? Review from previous lessons - What is interest? What are interest rates? What do they mean to the average person? What do they mean to you? Interest both paid and earned is one of the fundamental backbones of our financial system. How do people earn interest? What does it mean to earn interest/pay interest. What does interest mean to banks?

Background Information

In a previous lesson we spoke about something called ‘Interest’. Interest is an amount of money either paid or earned on money. If you borrow money from a bank to buy a car, you will pay interest on that money until it is paid back. If you deposit money in a bank and keep it there for a predetermined amount of time, the bank will pay you interest for allowing them to keep (and lend out) that money. Interest is usually given as a percentage rate and is almost always given as an Annual Percentage Rate or APR. Next time you see a car commercial or car dealership commercial, see if they use the term APR. That is in reference to many people who borrow money to buy new cars and pay for them over an extended period of time.

For the last 20 years or so, bank interest rates have been historically low which is great if you want to borrow money, but not as good if you have money saved that you would like to earn interest on. In Canada, the early 1990s was the last time we saw bank prime interest rates above 10%, and for the last decade it has been under 5%. This extended period of low rates has allowed many more people to borrow money to buy houses and build businesses. This, in part has contributed to the historic rise in housing prices in Canada over the last 30 years. You may have heard adults in your lives speak about how expensive it is to buy houses in BC, especially in the lower mainland and Victoria, well a long period of low bank interest rates has contributed in part to that outcome. Without going into the complex economics of government fiscal policy (how the government controls and manages their currency) the basic idea is, when interest rates are lower, people tend to borrow more money, when they are higher, this incentivizes people to save money.

Video – MsMM – What are Interest rates and why should you care about them.

Lesson – Calculating Interest Rates

How to calculate interest earned or interest payable. Calculating interest is a lot like calculating taxes, interest is a percentage based calculation on a total amount of money either borrowed or deposited. We will begin by looking at earning interest on money deposited.

Earning interest

The basic calculation for earning interest from a bank looks like this. A person may have some extra money saved that they don’t plan to spend anytime soon. So they head to their bank and ask what they can do with it. The client wants their money to be 100% safe so this rules out investments such as stocks, bonds or mutual funds. The main bank investment product for earning interest is called a Guaranteed Investment Certificate (GIC). They work like this, the more you deposit and the longer you leave it on deposit, the higher the interest rate. If you want a GIC that is cashable at any time and you only have a small amount to invest like $1000, the bank will offer you the lowest rate. If you have $1,000,000 to invest and you are willing to lock it in and not spend it for at least a year or longer, the interest rate offered will be higher. If you lock your money into non-cashable GIC and you decided you would like to cash it out early, usually you will forfeit any interest you should have earned as a penalty. You still get your money back, but because you cashed in the investment early, you don’t earn any interest. Let’s look at a basic interest calculation.

Calculating interest earned

Amount invested (put on deposit) $1000 . Interest rate 2% annually. We know from our tax calculations that 2% as a decimal would be listed as 0.02 so multiplying $1000 by 0.02 = $20 . If you leave your $1000 on deposit for the entire year and withdraw it when the one year term is up, they will give you your $1000 back plus $20 in interest for a total of $1020.

Calculating interest paid

If you borrow $1000 and the interest rate is 4% and the money is to be paid back at the end of one year, then at the end of that year you owe $1040. It’s really the same calculation but in one instance you have the money so the interest is paid to you and in the other the bank has the money and is lending it to you so the interest is paid to the bank. In reality when people borrow money they usually go in a payment plan and pay it back in installments and the bank calculates the interest owed on a daily basis, but this is more complicated than we need to go into at this point.

We learned about calculating simple interest in previous lessons, but now we are going to introduce interest calculation formulas.

Simple Interest formula

Simple interest earned can use the simple formula Interest earned = Principle x Interest Rate x Time (in years) or I = P x R x T

For example: $1500 invested at 5% annual interest rate for 3 years would earn $225.

1500 x 0.05 x 3 = 225

You can rearrange the formula for whatever variable you are missing. The 4 versions of this formula are listed on the Simple Interest calculation worksheet. This Simple Interest formula assumes either we are removing the interest earned every year or that the earned interest is only in relation to the principle itself. Next we will look at a more realistic example, compounding of interest over time, where interest earned begins to earn interest on itself.

Compounding of Interest (this topic can be covered as the teacher sees fit)

Where it gets really interesting is when interest is compounded over several years. Compounding simply means that the interest paid, if left in the investment, begins to then earn interest itself. In our previous example, let’s say the $1000 we are investing we will be locking that in for 5 years but instead of taking the interest out each year we leave it in. Because we are leaving the money with the bank for longer, they usually pay higher interest, let’s say they will now pay 3%. This is how the calculation will work:

Year 1: $1000 x 1.03 = $1030 this is what you have after one year.

Year 2: $1030 x 1.03 = $1060.90 this is what you have after year 2 because your $30 worth of interest from year 1 has also earned a little interest itself (90 cents) which then gets added to the total.

Year 3: $1060.90 x 1.03 = $1092.73

Year 4: $1092.73 x 1.03 = 1125.51

Year 5: $1125.51 x 1.03 = 1159.27

So after 5 years you get you $1000 back along with $159.27 in interest. $9.27 of that is the compounding effect of interest earning interest on itself.

There is a simple compound interest formula you can use that looks like this:

A = P(1 + r)^t

A is the amount you end up with

P is the principal (the amount you start with)

R is the interest rate as a decimal

T is the number of compounding periods

Activity/In-class work

Simple interest and compound interest worksheets. Have students do problems and review as a class.

Wrap-up/Extension

Have students find an online mortgage calculator and input a fixed amount for the loan but change the interest rate - what do they notice happens, have them change the amortization (the amount of time the loan is paid back over) what do they notice. If they start with a $500,000 mortgage amount with a 25 year payback period, at 5% interest, what are the payments. If the interest rate went down by 1% how much more money could they borrow and still have the payments be the same? What if the rate drops by 2%. This should demonstrate the immense power of compounding interest over time.