Compound Interest Calculator

Compound interest is a mechanism where interest generates further interest. Each time the interest is added to the remaining balance, the next calculation will be based on a larger total amount, so the money grows faster the longer it's invested.

This calculator allows you to calculate future value based on your initial investment, rate of return, frequency of compounding and number of years. You can also perform calculations in reverse, for example to find out what rate of return is required. If any field is left blank, that value will be calculated. You can also add regular deposits to see how the money grows along with the original capital over time.

What is compound interest?

With simple interest you get a fixed amount of interest in each period and the calculation is always based on the original principal. With compound interest the interest earned in each period is added to the remaining balance so that this interest also earns further interest in the next period. This feedback mechanism means that savings, investments and debts grow not linearly but exponentially. It has often been said that Albert Einstein called compound interest the eighth wonder of the world: "He who understands it can use it; he who does not understand it must pay for it."

These effects are small at first but become very significant over time. A balance that grows by 7% changes little in the first year, but because interest is calculated on the previous amount each year, it doubles after about ten years and quadruples after twenty. The two factors you can control yourself are time and frequency, and this calculator allows you to intuitively feel how important each one is.

The formula for compound interest:

The future value of a lump sum investment is the capital amount multiplied by (1 + interest rate per period) raised to the number of periods.

In this formula, $A$ is the final amount, $P$ is the original principal amount, $r$ is the annual interest rate expressed as a decimal number, $n$ is the number of times per year that the interest is compounded, and $t$ is the number of years. The interest earned is equal to the difference between the final amount and the principal amount.

Example calculation:

Suppose you invest $10,000 at an interest rate of 5 percent with the interest added to the principal each month for a period of ten years. The monthly interest rate is the result of dividing 5 by 12 and the number of periods is the result of multiplying 12 times 10 which equals 120.

The account balance is $16,470.09 and the interest earned is $6,470.09. Note that at a 5 percent rate of return, simple interest would only pay out $500 per year, for a total of $5,000 over ten years. The additional $1,470 is the effect of compound interest, which accrues every year as long as the money stays invested.

Compounding frequency - why it matters:

Even with the same annual interest rate, results can vary depending on how often interest is calculated. With compound interest, each calculation is based on a slightly higher account balance, so more frequent calculations tend to be slightly better. The difference between annual and monthly compounding is relatively large, while the difference between monthly and daily compounding is very small. This is because there's an upper limit, called continuous compounding, and decreasing the interval only makes you approach that limit gradually.

Continuous compounding is the limit that is reached when the number of periods goes to infinity, and it can be expressed by a simple formula involving the constant e (approximately equal to 2.71828).

The effective annual interest rate (APY)

Because the result depends on how often interest is compounded, it's not possible to determine the true return based on the stated rate alone. The effective annual rate (also called APY) is an annualized return that reflects the effects of compounding in a clear yearly figure. It answers the simple question: What percent increase will my balance actually be after one year with monthly compounding? The formula is:

If a 5 percent interest rate is compounded monthly, the APY will be about 5.12 percent. So an account with 5 percent interest that compounds monthly will earn more than one with 5 percent interest that only compounds annually. The APY is important when comparing savings accounts because it already takes into account the effects of compounding. This is similar to the APR (annual percentage rate) for borrowers. While the APR usually gives a nominal interest rate without taking compounding into account, the APY shows what the return will be after factoring in compounding, so a loan's APR can differ from its actual annual cost.

Add regular deposits

Most people do not pay a lump sum but make regular payments. When regular payments are entered, the calculator adds each payment to the balance at the end of the corresponding period and then calculates interest from that point forward. This is similar to how an annuity works. The earlier a sum of money is invested, the longer it has to grow, which makes it more effective than later investments. That's why it pays to start early. The future value of a stream of payments follows an annuity formula.

Here $PMT$ is the amount added to each period. The sum of future value consists of growth in this amount and growth in original deposit. In a graph, the increase is represented as a band that widens continuously while the area for interest curves upwards and eventually exceeds the entire invested amount by far.

Comparison of simple and compound interest

Two people each borrow $100, with an annual interest rate of 10%. The first person receives a fixed amount of $10 per year (simple interest). The second person receives compound interest on the increasing balance, so that the annual 10% is calculated against the current account balance.

Although the two individuals start out with almost no difference, after 40 years the second individual has about nine times as much money as the first. The difference comes from the fact that interest itself generates more interest. This is why patience in compounding interest is so important. You can check the difference using your own values by using the "Compare to simple interest" option on this calculator.

Calculating interest rate, term or initial capital

When dealing with compound interest problems it is often necessary to work backwards. You may know the future value you want and need to figure out what that requires in terms of time, rate or present value. Leave the unknown variable blank and enter the three known variables into the calculator and it will re-arrange the formula and calculate your missing variable. There are three types of compound interest calculations:

The last formula uses the natural logarithm to compute the time. It determines how long it takes for an amount of 10,000 to reach an amount of 25,000 assuming that the interest rate remains constant at 8 percent. These calculations only apply to the initial deposit amount. For regular deposits one has to calculate rates and periods under the assumption of continuous deposits which is possible in reverse direction only due to the lack of a simple closed solution.

The Rule of 72:

To quickly calculate how long it takes for an amount to double in size, divide 72 by the interest rate. At a 6 percent interest rate, it would take approximately 12 years for your money to double if you divide 72 by 6. At a 9 percent interest rate, it would take about 8 years. This is an approximation that works best with single-digit or low two-digit interest rates but serves as a useful sanity check on the exact values this calculator provides.

Where does compound interest occur?

Compound interest has both advantages and disadvantages. In the case of savings it is an advantage. Retirement accounts, index funds, and high-yield savings accounts all grow through compounding, and the earlier you start, the greater the effect of compounding will be in later years. With loans, however, it works against you. Credit cards charge interest daily on the outstanding balance, so the remaining debt grows exponentially just like with savings, but in the opposite direction. The logic is symmetrical. Take advantage of compound interest and avoid using it against yourself.

Limits and assumptions

This calculator assumes a constant interest rate, equal deposits and no taxes or fees charged over the period. Reality is more complex. The return on an investment varies from year to year and does not always hold the same interest rate. Savings rates also change. If the account has tax benefits, then taxation of interest earnings can have a significant impact. Inflation quietly erodes the purchasing power of future balances so that even a large number in thirty years may be worth less than the nominal amount shown. Note that results are to be understood as mathematical estimates and not guaranteed outcomes.

To calculate compound interest in excel or google sheets, do the following:

Enter the principal amount in cell B1, the annual interest rate in B2, the number of periods per year in B3, and the number of years in B4. You can then calculate the future value of a lump sum investment using one of the following methods:

The FV function uses the interest rate and number of periods for each period. So you need to divide the annual interest rate by the compounding frequency, and multiply the years by the compounding frequency, just like in the formula.