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Compound Interest Calculator

WOWA Simply Know Your Options

Inputs

Starting Investment

$

Periodic Investment

$

Contribution Frequency

MonthlyQuarterlyAnnually

Time Period

Years

Estimated Interest Rate

%

Compounding Frequency

DailyMonthlyQuarterlyAnnually

Results

Total Investment

$19,186

Total Investment

$19,186

Total Interest

$8,186

Total Principal

$11,000

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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!

• 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.

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.

If you're earning compound interest on an investment, it works for you because your money is growing. However, compound interest can also work against you if you are borrowing. If you're paying compound interest on a loan, 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 card debt.

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.

To expand on this, A is the future value of your investment, which is the amount that a compounding calculator would calculate for you. This includes your initial principal and the interest you earned. P is your initial principal, r is your interest rate in decimal form, and t is the number of years for which you want to calculate. 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.

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.

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. 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! A monthly compound interest calculator can be used to calculate for more months.

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 this new balance. At the end of the month, your account balance would be $1,008.37 - just slightly higher than with monthly compounding. 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 over a longer time period, the larger the effect that compounding will have.

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.

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! If the interest is compounded daily, the EAR would be even higher. 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

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.

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.

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.

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).

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.

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.

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.

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.

The exception to this is TD Credit Cards. TD Bank announced in 2020 that it will start adding unpaid interest to the credit card balance at the end of each statement period. Scotiabank also charges compound interest on the Scotia Momentum Mastercard. For this credit card, the unpaid interest is added to next month's statement, and interest is charged on it. To find out how your credit card issuer calculates interest and whether or not interest is compounded, review your cardholder agreement.

This is different from the United States, where most credit card issuers charge daily compounding interest.