Compound Interest Calculator
About the Compound Interest Calculator
This compound interest calculator uses compounding to calculate how much your investment will grow over time with compound interest. To do so, you will need to select a compounding frequency. This is how often interest will be compounded. You can also choose to make regular contributions. This will calculate the future value of your investment with compound interest, taking into account the regular contributions you make.
Compound interest allows the value of your investment to grow exponentially, and it's one of the most powerful tools available to investors. This compound interest calculator can help you see how your investment will grow over time and how different compounding frequencies can impact the growth of your investment. By making regular contributions, you can also see how much faster your investment will grow. Try out different scenarios to see the magic of compounding!
Compound Interest Calculator Terms
- Periodic Investment: How much money you will regularly contribute.
- Contribution Frequency: How often you will make your additional contributions.
- Estimated Interest Rate: The expected annual interest rate for your investment.
- Compounding Frequency: How often interest will be compounded for your investment.
- Total Principal: This is the amount of your total contributions.
- Total Interest: This is the total interest earned on your contributions.
What Is Compound Interest?
Compound interest is the interest you earn on both your original investment and the interest that has accumulated over time. In other words, compound interest is "interest on interest." The other way that interest can be calculated is called simple interest, in which interest accrues only on the initial principal. Since you earn interest on past earned interest with compounding, your investment or savings return will be higher than with a simple interest calculation.
While compounding is a powerful tool for investors and savers, compound interest won’t magically accelerate your return. Another key factor to compounding is time. The longer your money is invested, the greater the return, as you will have more time for your accumulated interest to earn even more interest.
Compound interest can work for you or against you, depending on if you are saving or borrowing. If you're paying compound interest on a loan, it's working against you because you're accruing more debt. For example, most U.S. credit card issuers may calculate your interest charges by compounding daily. However, that’s not the case in Canada. Most Canadian credit card issuers do not compound interest on credit cards.
If you're earning compound interest on an investment, it's working for you because your money is growing. This compound interest calculator is designed for investors and savers looking to see how much interest they can earn on their investment with compounding.
How to Calculate Compounding Interest
To calculate compound interest, you need three pieces of information:
- The principal: This is the starting sum of money on which you'll earn interest. In other words, it's the amount of money that you initially invest.
- The interest rate: This is the interest rate that your investment or savings would earn. It can be given as an annual rate, but you'll need to convert it to a periodic rate in order to calculate compound interest correctly.
- Estimated Interest Rate: The expected annual interest rate for your investment.
- Compounding Frequency: How often interest will be compounded for your investment.
- Total Principal: This is the amount of your total contributions.
- Total Interest: This is the total interest earned on your contributions.
Compound Interest Formula
Where:
- A = Final Amount
- P = Initial Principal
- r = Interest rate
- n = Compounding frequency per year
- t = Number of years
To expand on this, A is the final amount of your investment, which is the amount that a compound interest calculator would find for you. This includes your initial principal and your interest earned. P is your initial principal, r is your interest rate in decimal form, and t is the number of years that you want to calculate for. The value n would be the number of times that interest would be compounded per year. For example, monthly compounding would result in interest being compounded 12 times per year.
| Compounding Frequency | Number of Compounding Periods per Year |
|---|---|
| Daily | 365 |
| Monthly | 12 |
| Quarterly | 4 |
| Annually | 1 |
To see an example of how to calculate compound interest, let's say that you invest $1,000 at a 5% annual interest rate, and you want to know how much money you'll have after 20 years. Assume that compound interest is being paid yearly, which would cause n to be 1 in our compound interest formula. The number of years, t, would be 20. The compound interest equation would then be:
Based on this calculation, $1,000 invested for 20 years at a 5% annual interest rate would turn into $2,653.30 with annual compounding.
Daily vs. Monthly Compound Interest
The difference between daily and monthly compounding is the frequency with which interest is calculated. With monthly compounding, interest is calculated once per month. If you have a $1,000 investment that earns 10% annual interest, your account balance would be $1,008.33 at the end of the first month. This is because a 10% annual rate turns into a 0.833% monthly rate, which would be our periodic rate in the calculation. The next month, interest would be calculated on the new balance of $1,008.33, resulting in a balance of $1,016.73 (from $1,008.33 + $8.40) at the end of the second month.
A monthly compound interest calculator can also be used to find these numbers. Note that the first month earned $8.33 from interest, but the second month earned $8.40 from interest. The extra $0.07 interest earned is due to compounding!
With daily compounding, interest is calculated 365 times per year (or 366 times during a leap year). Applying the same example above and using a daily compound interest calculator, the daily interest rate would be 10% divided by 365, which is 0.0274%. Using this periodic rate, your account balance would be $1,000.274 after the first day. The next day, interest would be calculated on the new balance of $1,000.274. This process would continue until the end of the month, when your account balance would be $1,008.37 - just slightly higher than with monthly compounding.
This means that you would earn $8.37 in your first month with daily compounding. In comparison, monthly compounding would have earned you $8.33 in your first month. By compounding daily instead of monthly, you would earn an extra $0.04 in one month on a $1,000 investment. While the difference between daily and monthly compounding may seem small, it can have a big impact over time. The more often interest is compounded, the faster your account balance will grow. The longer you let your investment grow with a longer time period, the larger the effect that compounding will have.
Nominal Interest Rate vs. Effective Interest Rate
When you're saving or investing money, it's important to understand the difference between the nominal interest rate and the effective interest rate. The nominal interest rate is the stated rate. It does not take into account the effect of compounding. The effective interest rate is the actual rate of return that you receive, taking into account compounding. It's often called the annual percentage yield (APY) or effective annual rate (EAR).
The effective interest rate is always higher than the nominal interest rate. That's because with compounding, you're not only receiving interest on your original principal, but also on the accumulated interest from previous periods.
Effective Annual Rate Formula
Where:
- EAR = Effective annual rate
- r = Interest rate
- n = Compounding frequency per year
Calculating the Effective Annual Rate
Using the effective annual rate (EAR) formula above, we can find out how compounding can affect your real rate of return. Let’s take a look at a savings account that offers a 5% nominal interest rate with monthly compounding.
Using the EAR formula:
By compounding interest monthly, a 5% stated annual rate turns into an effective interest rate of 5.116%. That extra 0.116% annual return is due to compounding!
What if the bank offers daily compounding on this savings account? Since we know that more frequent compounding periods will increase your rate of return, we can expect the effective annual rate to be even higher.
With daily compounding, a 5% nominal rate turns into an effective rate of 5.127%. While the difference between daily and monthly compounding might not seem remarkable, this 0.011% extra return per year is money that you would otherwise not earn with a less frequent compounding period. The table below compares the effective annual rate for a variety of compounding frequencies based on a nominal annual rate of 5%.
Comparing Effective Annual Rate by Compounding Frequency
For a 5% Nominal Annual Rate
| Compounding Frequency | Effective Annual Rate |
|---|---|
| Daily | 5.127% |
| Monthly | 5.116% |
| Quarterly | 5.094% |
| Annually | 5.000% |
Continuous Compounding Interest
Continuous compounding is the idea that interest will compound constantly. By shortening the gaps between compounding periods, from minutes to seconds and even less, the effective annual rate eventually reaches a point where interest is compounded continuously.
Continuous Compounding Interest Formula
Where:
- A = Final amount
- P = Initial principal
- e = A constant that is roughly 2.71828
- r = Interest rate
- t = Number of years
While you would be hard-pressed to find a bank that pays continuous compounding interest, the idea of continuous compounding is used in finance. For example, the Black-Scholes options pricing model uses the continuously compounded risk-free rate of return to discount the option's strike price.
Compound Annual Growth Rate (CAGR)
The compound annual growth rate, known as CAGR, is the rate of return that an investment earns each year over a given period of time. CAGR is a good way to compare investments with different starting and ending values, as well as different time periods. To calculate CAGR, you will need to know the value of an investment at the end of the period and the value at the beginning of that period. CAGR is the required compounded growth rate that grows your initial investment to a certain final value.
CAGR Formula
Where:
- t = Number of years
Rule of 72
The rule of 72 is a way to quickly estimate how long it would take to double your money at a certain interest rate. More specifically, the rule of 72 requires interest to be compounded annually. The number of years it will take to double your money is found by dividing 72 by the interest rate. For example, if you had an interest rate of 9%, it would take 8 years for your money to double (72/9 = 8).
Rule of 72 Formula
Where:
- t = Number of years to double your money
- r = Annual interest rate
Rule of 69, Rule of 70, or Rule of 72?
The Rule of 72 would be used for annual compounding, and it is the most commonly used formula. However, other compounding frequencies would require a different formula. That’s because more frequent compounding would cause the investment to double quicker.
Continuous compounding would use the Rule of 69. Daily compounding would use the Rule of 70. However, in most cases, the Rule of 72 would be a good estimate for most investments.
| Compounding Frequency | Rule Type | Time to Double Formula |
|---|---|---|
| Continuous | Rule of 69 | t = 69/r |
| Daily | Rule of 70 | t = 70/r |
| Annual | Rule of 72 | t = 72/r |
Comparing Doubling Times
Let’s say that an investment has an interest rate of 5%. How long would it take to double your investment under the different compounding frequencies? As seen in the table below, it would take 14.4 years to double with annual compounding. With continuous compounding, you would double your money in 13.8 years.
| Compounding Frequency | Rule Type | Time to Double Formula |
|---|---|---|
| Continuous | t = 69/5 | 13.8 years |
| Daily | t = 70/5 | 14.0 years |
| Annual | t = 72/5 | 14.4 years |
Compound Interest in Canada
Mortgages
Mortgages are compounded semi-annually in Canada when calculating mortgage interest for fixed-rate mortgages. However, some lenders may compound interest more frequently for variable mortgages. This means that your effective annual rate (EAR) will be higher than your quoted mortgage rate.
Credit Cards
Most Canadian credit card issuers do not charge compounding interest on credit card balances. Instead, interest is calculated daily and charged monthly. If you do not fully pay off your credit card balance, then interest will not be charged on this accumulated interest. In other words, interest is usually not compounded on Canadian credit cards. The exception to this is TD, which announced in early 2020 that it will start charging compound interest on TD credit cards.
Scotiabank also charged compound interest on the Scotia Momentum Mastercard. For this credit card, Scotiabank adds unpaid interest to your next month's statement. This means that they will charge interest on interest. To find out how your credit card issuer calculates interest and whether or not interest is compounded, review your cardholder agreement.
In Canada, the average daily balance is used to calculate your credit card’s interest charges. It’s the sum of each day’s balance divided by the number of days in that statement month. For example, if you had a balance of $100 for 15 days and $200 for 15 days in a month with 30 days, then your average daily balance would be $150. The interest charged would be based on your average daily balance of $150. Since interest is not compounded or charged daily, your average daily balance is not affected by interest charges.
This is different from the United States, in which most U.S. credit card issuers charge daily compounding interest. When calculating your average daily balance for an American credit card, each day’s balance is multiplied by a daily interest rate to get a daily interest charge. This daily interest is then added to your account balance, which means that the next day’s interest charge will compound on previous interest charges. This results in daily compounding of interest.