How to Calculate Compound Interest?
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Are you ready to harness the power of compound interest in your investment accounts? A financial advisor will help you pick between RRSPs, TFSAs, ETFs and a number of other ways to save for your future.
"Compound interest is the eighth wonder of the world. He who understands it, earns it... he who doesn't... pays it."
This quote is attributed, possibly falsely, to Albert Einstein. Whether he said it himself or not is irrelevant. Compound interest is a powerful force and you need to understand it to harness it in your investing.
Compound interest appears throughout financial products from savings accounts, guaranteed investment certificates (GICs) and retirement accounts to personal loans, mortgages and credit cards. The tool above will help you to calculate it so that you better understand the cost of borrowing and the power of long-term investing.
What is compound interest?
In simple terms, compound interest is “interest on interest”. This means interest is calculated based on the initial principal (the initial principal meaning the original sum of money lent or invested) and the accumulated interest from previous periods. As time passes, the interest rate on money lent or invested increases.
How is compound interest calculated?
Below is the formula for compound interest. It may look a little confusing, but we assure you that it's quite simple:
Good to know
Compound Interest Formula: A = P(1+r/n)^nt
Formula key:
- A = final amount
- P = initial principal balance
- r = interest rate
- n = number of times interest applied per period
- t = number of time periods elapsed
- ^ = to the power of
For example, let's take the example of a retirement account with $1,000 invested into it with an interest rate of 8%, this interest is then compounded twice a year or semi-annually. After 5 years, how much will the initial investment have increased by?
A = 1,000 (1+0.08/2) 2(5)
At the end of 5 years, the original investment in the retirement account will have increased to $1,480.24. You would have earned $480.24 in interest. This shows you the power of compound interest. That is without any additional investment. If you keep adding $1,000 each year once per year, your $6,000 investment would be worth $7,365.59!
Are you saving for retirement? It is never too early. Compound interest is most powerful when it has a long time to grow! A financial advisory can help you get started:
How to use our compound interest calculator:
To calculate compound interest, we have a free and easy-to-use compound interest calculator above. Simply enter the following values into the boxes provided:
- Initial investment
- Years
- Regular contributions
- Contribution frequency (once per month, once per quarter, twice per year or annually)
- Estimated interest rate
- Compound frequency (when)
Once all these details have been entered, our compound interest calculator will work out for you the total value of your investment and the total interest earned.
Simple vs compound interest:
The key difference between simple and compound interest is that simple interest is always based on the original principle when being calculated. For example, if there was an annual simple interest of 1% on $1,000 invested, you would receive $10 every year.
This is different from compound interest, where the first year of an investment, with a 10% interest rate, of $1,000 would give you $100. The next year you would receive 10% of $1,100, earning $110. The next year you receive 10% of $1,210, and so on.
Below is a table to illustrate the difference between simple and compound interest, on a $1,000 investment, both having an interest rate of 10%
| Years | Compound interest | Simple interest |
|---|---|---|
| 0 | 1,000 | 1,000 |
| 1 | 1,100 | 1,100 |
| 2 | 1,210 | 1,200 |
| 3 | 1,331 | 1,300 |
What is the snowball effect?
The snowball effect is a term used to explain how compounding interests work. Imagine if you were to roll a small snowball down a hill, it would gradually get bigger and bigger. The bigger it gets, the more snow it can take on. As it gets bigger, its ability to get bigger grows with it. The same goes for compound interest rates. For example, as the value of investment gets bigger, so does the increase you receive. Small increases over time can compound and lead to a large increase in growth.
Retirement accounts and long-term investments depend on the snowball effect. Speak with a financial advisory to learn how the snowball effect can help you secure your financial future.
How often is interest compounded?
How often interest is compounded varies. Savings accounts typically compound daily or monthly. Although, some may compound semi-annually or quarterly. For example, when it comes to a savings account, the more interest is compounded, the more money is gained.
Fixed-rate mortgages compound semi-annually. This means that if you are making monthly payments, your mortgage interest is only being compounded twice a year. Whereas, a variable rate mortgage typically compounds monthly. This means that interest is added every month instead of once a year.
Credit card interest rates are most often compounded daily, making them an expensive method of borrowing for people who carry a balance.
How can compounding interest benefit you?
Compounding interests can have great benefits for your long-term savings accounts and investments. Your initial principle will become bigger in value, even though you are not adding anything to it yourself. You can make a lot of pure profit. It is also a good alternative to keeping your money in a low-savings account, which often will not increase as much as inflation per year. This means while your money is sitting in a low-interest account, it is losing its buying power.
One way you can maximize the benefits of compound interest is by starting as early as you can. The longer you invest, the more you will gain because of the nature of compounding interest. The more times it compounds, the larger the gain you will see on your savings account or investment.
Good to know
A simple investment tip: is to leave your savings account or investment untouched for as long as you can. By withdrawing money you are reducing the amount you could be gaining by simply leaving it alone.
How can compounding interest work against you?
Compound interest will work against you when it comes to things like credit cards and loans, such as mortgages. The longer you are making repayments on them, the more interest you are paying.
For example, mortgage repayments can last decades. Although your mortgage may only be compounded twice a year, the length of many mortgages means you will end up paying a lot of interest. The same is true for any sort of long-term loan.
Remember that the quicker you can make payments on loans and credit cards, the less interest you will be paying. The interest rate on credit cards can range as high as 18 to 29%. Let's use the example of someone who has a $200 credit card debt and pays back $40 a month, with an interest rate of 20%:
| Month | Debt |
|---|---|
| 1 | $192 |
| 2 | $182 |
| 3 | $170 |
| 4 | $157 |
| 5 | $140 |
| 6 | $120 |
| 7 | $96 |
| 8 | $67 |
| 9 | $32 |
| 10 | $0 |
Good to know
In this example, it cost the individual double the amount of the debt at $400 to pay it off.
What’s the law of 72?
The law of 72 is a formula that is used to estimate how long it will take for an investment to double. It is accurate for interest rates that range between 6% and 10%. The formula is shown below:
Good to know
Years required to double investment = 72/compound annual interest rate
For example, if an investment had a 6 percent annual compounded interest rate (72/6) it would take an estimated 12 years for the investment to double.
Let's use the example of $1,000 with an interest rate of 6%:
| Years | Value of investment |
|---|---|
| 0 | 1,000 |
| 1 | 1,060 |
| 2 | 1,123.60 |
| 3 | 1,191.02 |
| 4 | 1,262.50 |
| 5 | 1,338.23 |
| 6 | 1,418.52 |
| 7 | 1,503.63 |
| 8 | 1,593.85 |
| 9 | 1,689.48 |
| 10 | 1,790.85 |
| 11 | 1,898.30 |
| 12 | 2,012.20 |
