# Compound Interest Calculator

Calculate the future value of money using our compound interest calculator. Enter the present value, additional contributions (if any), interest rate, and length of time in years below.


per year
years

## Future Value:

 Total Value: $1,254.41 Total Principal:$1,000.00 Total Interest: $254.41 ### Balance by Year This calculation is based on widely-accepted formulas for educational purposes only - this is not a recommendation for how to handle your finances, and it is not an offer to lend or invest. Consult with a financial professional before making financial decisions. Learn how we calculated this below ## On this page: ## How to Calculate Compound Interest Compound interest is interest that is calculated on the principal value and accumulated interest of an investment or loan. Using a tool like the compound interest calculator will provide the quickest and easiest way to calculate compound interest. With compound interest, interest is earned on the prior interest earned and the principal balance. This differs from simple interest in that simple interest is only earned on the principal balance. Additionally, you can enter an amount for contributions. The assumption here is that this amount is added at the end of the year, so interest won’t be earned in the year that it is added. However, if more than one year is selected, it will earn interest in future years. Interest can also be earned on those contributions, leading to more exponential growth. ### The Importance of Compounding Frequency The frequency that interest is compounded can have a large effect on the growth over time. More regular compounding will result in faster growth since the growth is more exponential. This compound interest calculator gives the option for continuous, daily, monthly, quarterly, semiannually, and annually compounded interest, which are the most common and practical time intervals. Interest can technically be compounded at any time interval you would like, but the time intervals above are what you will most likely encounter and are provided in the compound interest calculator. The more frequent the compounding, the more interest will be paid. If you select “continuous” from the compounding dropdown in the calculator, it will yield the highest interest amount. Selecting “annually” will produce the lowest interest. Annual compounding makes it easier to calculate interest by hand since the formula is a bit simpler with annually compounded interest. ### Compound Interest Formulas There are several formulas for calculating compound interest, depending on the compounding frequency and whether you’ll be making contributions along the way. #### Compound Interest Formula with Annual Compounding The compound interest formula in its most basic form assuming compounding once per period is: A = P \times \left (1 + r \right )^{t} where: A = future value P = present value r = interest rate t = number of periods #### Compound Interest Formula for Compounding Multiple Times per Period The compound interest formula for interesting compounding multiple times per period and without contributions is as follows: A = P \times \left (1 + \frac{r}{n} \right )^{nt} where: A = future value P = present value r = interest rate n = number of times interest is compounded per period t = number of periods #### Compound Interest Formula with Annual Contributions However, if you want to add contributions at the end of each year, you would use the following formula: k = \left (1 + \frac{r}{n} \right )^{nt} A = P \times k + PMT \times \frac{k − 1}{\frac{r}{n}} where: A = future value P = present value PMT = annual contribution r = interest rate n = number of times interest is compounded per period t = number of periods ### Continuously Compounded Interest Formula Interest that is continuously compounded earns the most interest of all the time intervals because you are always earning interest. The continuous compound interest formula is: A = P \times e^{rt} where: A = future value P = present value e = Euler’s number – approximate value of 2.718281 r = interest rate t = number of periods ### Examples We will look at a few examples: one with no contributions, one with annual contributions, and one with continuous compounding. #### No Contributions Let’s say we will invest$10,000 for 3 years at an annual interest rate of 5% and interest will be compounded annually. (tip: you can also use our daily compound interest calculator). In this first example, we assume no contributions.

Using the second compound interest formula above, we start out with:

\$10,000 \times \left (1 + 0.05 \right )^{3} \$10,000 \times \left (1.05 \right )^{3}
\$10,000 \times 1.157625 \$11,576.25

#### Annual Contributions

Now if we use the compound interest formula with a $500 annual contribution, we get: k = 1.157625 A = \$10,000 \times 1.157625 + \$500 \times \frac{1.157625 − 1}{0.05} A = \$10,000 \times 1.157625 + \$500 \times \frac{0.157625}{0.05} A = \$10,000 \times 1.157625 + \$500 \times 3.1525 A = \$11,576.25 + \$1,576.25 A = \$13,152.50

If you compare the compound interest formulas above, you will see the second part of the formula without contributions can be substituted in place of the variable k in the formula with contributions so we don’t need to recalculate this portion of the formula.

So, while we contributed $1,500 ($500 per year for 3 years), the balance increased by $1,576.25 since we earned interest for 2 years on the first contribution and for 1 year on the second contribution. #### Continuous Compounding Using continuous compounding with the example above, we would get an amount equal to$11,618.34 as the calculation below shows. This is $42.09 higher than with annual compounding, but this value will increase over time. A = \$10,000 \times 2.718281^{0.05 \times 3}
A = \$10,000 \times 1.161834 A = \$11,618.34

## How Long Does it Take to Double an Investment using Compound Interest?

If you want to find the time it will take to double an investment using compound interest then you can use the Rule of 72. The Rule of 72 provides an approximation of the time to double by dividing 72 by the interest rate.

time\ to\ double = \frac{72}{rate}

For instance, it would take a little over seven years to double an investment with an annual rate of 10% (72 / 10 = 7.2).

The Rule of 72 is just an approximation, to find the exact time to double you can use our Rule of 72 calculator.

## How to Calculate the Total Value After Interest

Total value is the sum of principal and interest. The total principal is the sum of the initial value plus any contributions. The total interest is the amount of interest that was earned from the investment or accrued on a loan.

The examples above show how to calculate total value mathematically. As you can see, it is much easier to use a compound interest calculator.

You can also use our APY calculator if no contributions are made or our CAGR calculator to reverse the compound interest formula and show what the compounding interest rate would be if you know the ending balance.

### How to Calculate Total Principal

To calculate total principal, add the initial value to the product of the number of years and annual contribution. If there are no contributions, then the total principal is equal to the initial value.

In our first example, the total principal was $10,000 since there were no contributions. However, the total principal in the second example was$11,500 because $1,500 in contributions were added to the beginning principal of$10,000.

### How to Calculate Total Interest

Total interest is calculated by a three-step process:

1. Take the annual interest rate and divide by the number of times interest is compounded in a year and then add 1.
2. Raise this number to the power of the number of years times the number of times interest is compounded in a year and then subtract 1.
3. Multiply this new amount by the initial value.

While things get a bit more complicated when contributions are introduced, these are the steps needed to calculate compound interest.

You can also calculate compound interest using our interest calculator, which allows you to calculate either simple or compound interest.