How to Calculate Compound Interest. Compound interest is distinct from simple interest in that interest is earned both on the original investment (the principal) and the interest accumulated so far, rather than simply on the principal. Because of this, accounts with compound interest grow faster than those with simple interest. For example, if your interest compounds annually, that means that you’ll gain more interest in the second year after your investment than you did in the first year. Additionally, the value will grow even faster if the interest is compounded multiple times per year. Compound interest is offered on a variety of investment products and also charged on certain types of loans, like credit card debt.^{ }Calculating how much an amount will grow under compound interest is simple with the right equations.
Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
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What Is Compound Interest?
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
“Interest on interest,” or the power of compound interest, is believed to have originated in 17th-century Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount.
Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be.
KEY TAKEAWAYS
- Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.
- Generating “interest on interest” is known as the power of compound interest.
- Interest can be compounded on any given frequency schedule, from continuous to daily to annually.
- Compounding multiplies money at an accelerated rate.
How to Find Annual Compound Interest
Define annual compounding.
The interest rate stated on your investment prospectus or loan agreement is an annual rate. If your car loan, for example, is a 6% loan, you pay 6% interest each year. Compounding once at the end of the year is the easiest calculation for compounding interest.
- A debt may compound interest annually, monthly, or even daily.
- The more frequently your debt compounds, the faster you will accumulate interest.
- You can look at compound interest from the investor or the debtor’s point of view. Frequent compounding means that the investor’s interest earnings will increase at a faster rate. It also means that the debtor will owe more interest while the debt is outstanding.
- For example, a savings account may be compounded annually, while a pay-day loan can be compounded monthly or even weekly.
Calculate interest compounding annually for year one.
Assume that you own a $1,000, 6% savings bond issued by the US Treasury. Treasury savings bonds pay out interest each year based on their interest rate and current value.
- Interest paid in year 1 would be $60 ($1,000 multiplied by 6% = $60).
- To calculate interest for the second year, you need to add the original principal amount to all interest earned to date. In this case, the principal for year 2 would be ($1,000 + $60 = $1,060). The value of the bond is now $1,060 and the interest payment will be calculated from this value.
Compute interest compounding for later years.
To see the bigger impact of compound interest, compute interest for later years. As you move from year to year, the principal amount continues to grow.
- Multiply the year 2 principal amount by the bond’s interest rate. ($1,060 X 6% = $63.60). The interest earned is higher by $3.60 ($63.60 – $60.00). That’s because the principal amount increased from $1,000 to $1,060.
- For year 3, the principal amount is ($1,060 + $63.60 = $1,123.60). The interest earned in year 3 is $67.42. That amount is added to the principal balance for the year 4 calculation.
- The longer a debt is outstanding, the bigger the impact of compounding interest. Outstanding means that the debt is still owed by the debtor.
- Without compounding, the year 2 interest would simply be ($1,000 X 6% = $60). In fact, every year’s interest earned would be $60 if you did earn compound interest. This is known as simple interest.
Create an Excel document to compute compound interest.
It can be handy to visualize compound interest by creating a simple model in Excel that shows the growth of your investment. Start by opening a document and labeling the top cell in columns A, B, and C “Year,” “Value,” and “Interest Earned,” respectively.
- Enter the years (0-5) in cells A2 to A7.
- Enter your principal in cell B2. For example, imagine you are started with $1,000. Input 1000.
- In cell B3, type “=B2*1.06” and press enter. This means that your interest is being compounded annually at 6% (0.06). Click on the lower right corner of cell B3 and drag the formula down to cell B7. The numbers will fill in appropriately.
- Place a 0 in cell C2. In cell C3, type “=B3-B$2” and press enter. This should give you the difference between the values in cell B3 and B2, which represents the interest earned. Click on the lower right corner of cell C3 and drag the formula down to cell C7. The values will fill themselves in.
- Continue this process to replicate the process for as many years as you want to track. You can also easily change values for principal and interest rate by altering the formulas used and cell contents.
How to Calculate Compound Interest on Investments
Learn the compound interest formula.
The compound interest formula solves for the future value of the investment after set number of years.
Alternative: For a quick and easy method of calculating compound interest, use the continuous compounding formula. This formula allows you to calculate the maximum future value of your investment based on a theoretically infinite number of compounding periods within a given length of time.
The formula for calculating the amount of compound interest is as follows:
- Compound interest = total amount of principal and interest in future (or future value) minus principal amount at present (or present value)
= [P (1 + i)^{n}] – P
= P [(1 + i)^{n }– 1]
Where:
P = principal
i = nominal annual interest rate in percentage terms
n = number of compounding periods
Take a three-year loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be:
$10,000 [(1 + 0.05)^{3} – 1] = $10,000 [1.157625 – 1] = $1,576.25
Gather variables the compound interest formula.
If interest compounds more often than annually, it is difficult to calculate the formula manually. You can use a compound interest formula for any calculation. To use the formula, you need to gather the following information:
- Identify the principal of the investment. This is the amount of your initial investment. This could be how much you deposited into the account or the original cost of the bond. For example, imagine your principal in an investment account is $5,000.
- Locate the interest rate for the debt. The interest rate should be an annual amount, stated as a percentage of the principal. For example, a 3.45% interest rate on the $5,000 principal value.
- In the calculation, the interest rate will have to be input as decimal. Convert it by dividing the interest rate by 100. In this example, this would be 3.45%/100 = 0.0345.
- You also need to know how often the debt compounds. Typically, interest compounds annually, monthly, or daily. For example, imagine that it compounds monthly. This means your compounding frequency (“c”) would be input as 12.
- Determine the length of time you want to measure. This could be a goal year for growth, like 5 or 10 years, or this maturity of a bond. The maturity date of a bond is the date that the principal amount of the debt is to be repaid. For the example, we use 2 years, so input 2.
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