Compounding Interest – Why it is of interest …
One of the things that savings, loan payments, mortgages, KiwiSaver and the Consumer Price Index have in common is Compound Interest yet most people don’t know what it is and how it works. In fact, most people would say what has it got to do with me and why should I even care about compound interest at all?
If we take the example of a soon-to-be mum in her late twenties, the last thing you would imagine she would be interested in is an article about money or managing her finances. In reality, how does knowing this affect her baby and more importantly how does it help her navigate all the new challenges of motherhood? Read on to find out why it is important to understand the good and bad of compound interest.
Key Ideas:
- What is compound interest and why care?
- The formula for compound interest
- How compound interest grows over time
- The good and bad
What is compound interest and why care?
Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest”. It is interest earned from the original principal plus accumulated interest. Not only are you earning interest on your beginning deposit, you are earning interest on the interest. This will make a sum grow at a faster rate than simple interest, which is calculated only on the principal (or initial) amount.
You can think about compound interest a bit like what happens with the “snowball effect”. A snowball starts small, but as more snow is added, the bigger it gets. As it grows, it becomes bigger at a faster rate.
It has been acknowledged that no other single thing about money can build up or tear down your nest egg faster, or massively increase or decrease your mortgage than compound interest.
The formula for compound interest
I know it looks scary, but let’s break it down:
P is the future value
C is the initial amount (let’s say $100)
r is the interest rate (e.g. 5%)
t is how many years (e.g. 20 years)
N is how many times a year the interest is compounded (e.g. monthly, so 12 times)
[To try out how this works for you, go here, and use your own numbers. How much could you save over the next 5,10 or 20 years…?]
The answer, usging the numbers in our formula =
$271.26
[ If you prefer Excel, this is how you can work it out in a spreadsheet =100*(1+(5%/12))^(12*20) ]
So what is this actually saying?
We started with $100. And invested it for 20 years with an interest rate of 5% per year. The interest is calculated monthly. Therefore, with interest, on interest, on interest… month after month, year after year, we get to $271.36.
To understand compound interest, start with the concept of simple interest: You deposit money, and the bank pays you interest on your deposit.
For example, there are 12 months in the year, so that 5% is divided by 12, and then applied monthly. This then happens for the next 20 years. So if you earn 5% annual interest, a deposit of $100 would gain you $5.12 after a year. What happens the following year? That’s where compounding comes in. You’ll earn interest on your initial deposit, and you will earn interest on the interest you just earned.
The interest your money earns the second year will be more than the year before, because your account balance is now $105.12, not $100. The interest is then calculated on that new amount (the accumulated amount) rather than on the initial investment of $100. With compound interest, even if you don’t make any additional deposits, your earnings will accelerate.
Although, this example shows a compounding frequency of monthly, you may see other frequencies. Typically, a mortgage is calculated with a compounding frequency of daily, so 365 days a year. This marginally increases the amount of interest collected by the banks.
On the example above, if we used daily compounding over 20 years, the end amount at year 20 would be $271.81. Now you may think that a difference of $0.55 cents ($271.81 – $271.26) is not much to worry about, but when you are a bank dealing in millions of dollars of loans, those ‘small amounts’ add up to a lot !
Debt can also compound, if you are borrowing money, compounding works against you and in favour of your lender instead. You pay interest on the money you have borrowed. The following month, if you haven’t paid the amount you owe in full, you will owe interest on the amount you borrowed plus the interest you have accrued. The slower you repay a debt which charges interest, the more you will end up paying back over time.
The good and bad
Compound interest can work for you, but it can also increase the cost of your debt. It can erode your hard work. It can make the value of your money appear to vanish, due to inflation. It can also work in your favour and over time and give you a bumper retirement fund in something like Kiwisaver.
The best compounding happens when any interest we earn gets reinvested and earns even more interest. It is interest earning interest, and our money is working for us instead of us working for it!
The amount of money you start with does not affect compounding. Whether you start with $100 or $1 million, compounding works the same way. The results seem bigger when you start with a large deposit, but you aren’t penalized for starting small or keeping accounts separate. It’s best to focus on percentages and time when planning for your future: What rate will you earn, and for how long? The dollars are just a result of your rate and timeframe.
The longer you leave your money, the more powerful the compounding interest effect. So, the earlier you can start saving, the more you make from compound interest (of course, only if we don’t withdraw the interest). That is the concept that KiwiSaver works on.
The same applies to other investments such as shares, where we regularly reinvest dividends, or when the company reinvests its profits.
Withdrawals and deposits can also affect your account balance. Letting your money grow or regularly adding new deposits to your account will work best. If you withdraw your earnings, you dampen the effect of compounding.
As we have seen compound interest is an essential concept to understand when managing your finances. This is especially true if we go back to the example at the start, as to why a soon-to-be mum in her late twenties would want to know and understand the affects it could have on her, the baby and her financial future.
As we’ve shown, compound interest can help you earn a higher return on your savings and investments. The other side of the coin is that it can also work against you when you’re paying interest on a loan. As a young mum you want to start saving early so your money works for you and you want to be in the situation where you can be paying off any debt without interest compounding. Knowing how compound interest can work both for and against you allows you to have a better grasp and control over your financial situation.
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Dominic started Bolster Risk Management to help people along their personal finance journey.
He believes that personal insurance is the bedrock to financial security and wealth creation. You have to protect your greatest asset, your ability to earn an income.
Underpinning this is a philosophy that says Your Money Matters.