Simple vs compound interest

Not all interest is created equal, and it all comes down to mathematics.

There are two main types of interest: simple and compound interest. So how do they work, and what's the difference between them?

What is interest?

First up, it's important to grasp the concept of interest before diving into the different types.

In basic terms, interest is the cost of using somebody else's money and works in two ways. When you borrow money, you pay interest. When you lend money, you earn interest.

Interest earned

If you deposit money into your bank account, interest is what you earn for keeping it there. It will be expressed as a percentage of the deposit. The bank will do its best to encourage you to leave your money in your account so they can use it to lend to others (at a higher interest rate) or invest. Banks frequently change savings account interest rates to entice new depositors as well as make it attractive for existing depositors to keep their money there.

Interest paid

If you take out a loan or use a credit card, interest is the percentage of your balance that you pay to access money that's not yours. Essentially, you give the lender more money than they lent you. Home loans are a prime example. Borrowers can pay hundreds of thousands of dollars in interest over the course of a loan.

What is simple interest?

As a saver, simple interest, sometimes known as nominal interest, is interest earned on the money you've deposited into an account - the principal - not on the interest it's earning.

Alternatively, if you're borrowing money, you will always repay the interest first and then the required principal.

Below is the mathematical formula used to calculate the total cost of a simple interest loan:

A = P (1 + Rt)

Formula	Explanation
A	the total accrued amount (principal + interest)
P	principal amount
I	interest amount
R	rate of interest (as a percentage or decimal)
t	time period involved (annually/monthly)

If you're a bit daunted by the maths, we'll break it down simply.

Let's take the example of Anna. She's just graduated from university and needs a decent car to get to work. She takes out a $10,000 personal loan to pay for the car. The bank is offering her a 5% p.a. interest rate and she's going to take three years to pay off the loan.

In the example:

• A = Total cost of the loan = P + I

• P = $10,000 loan

• I =?

• R= 0.05 (converted from a percentage to a decimal)

• t = 3 years

So, A = $10,000 (1 + 0.05 x 3)

A = $10,000 x (1.15)

A = $11,500

That means Anna would have to repay $11,500 in total. If we wanted to just calculate how much interest she was paying, the formula would be:

I = A - P

I = $11,500 - $10,000

I = $1,500

Just as in the example above, simple interest is commonly used for loans including home loans, car loans, and personal loans. Term deposits also often use simple interest, while savings accounts tend to use compound interest.

What is compound interest?

Now, we've gone through the primary school maths of simple interest; hopefully we're ready for compound interest which is a bit more secondary school.

In 2010, the world's most revered investor Warren Buffet was quoted as saying, "My wealth has come from a combination of living in America, some lucky genes, and compound interest."

It's also reported Albert Einstein nominated compound interest as the eighth wonder of the world, although that's the subject of debate.

Regardless of whether Einstein said this or not, there's no denying the power of compound interest. It is interest paid on the principal as well as the accumulated interest on money you invested or borrowed in the first place.

As a depositor, it means you earn interest on your initial deposit and the amount it's increased by as you keep earning interest. It's much like the hygienic financial version of double-dipping.

Compound interest is calculated using the following formula:

A = P (1 + r) (n)

We're using the same abbreviations as before, except A is for final balance (deposit plus interest earnings), P is for the deposited amount, and the added 'n' represents the number of times that interest is compounded.

Let's revisit Anna. After teaching for several years, she's managed to save $5,000 and has decided to invest it for some extra income. She's putting it into an account which compounds monthly (which is one of the most common) at 5.00% p.a. and won't make any additional payments for a three-year period (36 months). First, however, we need to divide the annual interest rate by 12, to get the monthly rate, which comes to 0.00416.

A = $5000 (1.00416)36

A = $5000 x 1.1611

A = $5,805

If we break that figure down further, Anna earned $255.81 interest in her first year, $268.90 in the second and $282.65 in the third and final.

If that one got too complex for you, there are many online calculators that can do this for you and also break down the figures into graphs if you're after more information.

Which interest reigns supreme when it comes to savings?

This one is far more clearcut than Batman vs Superman, Holden vs Commodore, Celtic vs Rangers.

In fact, it's a bigger mismatch than the Socceroos beating American Samoa 31-nil in a 2002 FIFA World Cup qualifier.

When it comes to simple vs compound interest, there is daylight between them. Just check the graph below:

Simple interest is much like a domino effect while compound interest is more of a snowball. Simple interest will continue to tick over, each year yielding the same interest again and again. Compound interest will yield interest that continues to increase the longer it's left to its own devices, much like a rolling snowball, gaining in size over time.

As you can see in the graph above, compound interest dwarfs simple interest in the profits it can generate. It's a no brainer that if you're given the decision to choose between the two for interest you can earn, you would opt for compound. But for the interest you pay, simple interest is more beneficial to your financial outcome.

Simple interest is simple by name and simple by nature. However, while compound interest is a lender's best friend, you're not always going to be the lender. A credit card is one product that uses compound interest to maximise its profits and the interest you pay.

Savings.com.au's two cents

Interest can be a dry topic, but it's a big part of what makes the economy go round. Being oblivious to how it's calculated can set you up for financial stress while having even a basic understanding of its workings can give you a leg up, with very little effort required.

Term deposits are an example of a simple interest product (although not all of them). The opportunity for compounding comes if you reinvest the principal and interest you are paid after one term into another term deposit, thereby earning interest on that interest.

The thing to remember about compound interest is that time is of the essence. If you are paying compound interest as a borrower, do what you can to reduce what you owe as it will cut down how long you are required to pay interest. If you are a saver, make a deposit as early as you can, even if it's small. Keep adding to it when possible - and leave it to snowball.

Photo by Todd Quackenbush on Unsplash