Compound Interest Calculator

The Compound Interest Calculator finds the amount of compound interest, or interest on interest, you can earn based on an initial investment, monthly contributions, interest rate, and length of time. The compound interest chart below shows how much faster the accumulated interest in your account grows compared to your initial investment and monthly contributions. Check out the compound interest table to see exactly how much interest you can earn every month.

How do you calculate compound interest?

If you're interested in the math, use the following compound interest formula to calculate the total compound interest earned over time:

$$\textbf{A} = P(1 + \frac{r}{n})^{nt}$$

Where:

• A: Total account balance. This includes your initial investment, any deposits added to your account, and any interest you previously earned.
• P: Principal. This is your initial investment and any deposits you added to your account.
• r: Annual interest rate as a decimal, or the annual interest rate as a percentage divided by 100.
• n: Number of compounding periods, or how often the interest is calculated based on your balance. With monthly compounding, interest is calculated for your account 12 times in a year, so n = 12.
• t: Time in years, as a decimal or fraction if there is a partial year. In the example below, we will calculate compound interest each month, so t = ¹⁄₁₂.

Next, we can find the total amount of interest earned using this equation:

$$\textbf{Total Interest Earned} = A - P$$

Example

Let's walk through the example above step-by-step for the first few months so you can see how compound interest is calculated. Keep in mind we assume all deposits are made at the end of the month and interest is compounded monthly.

Month 1: At the end of the first month, your account balance is $1,000. You won't earn interest on that $1,000 until the end of the next month, and you also haven't started your monthly deposits yet.

Month 2: At the end of the second month, you have earned interest for the $1,000 you originally added to your account. Let's use the compound interest formula above to calculate your account balance at the end of Month 2 where:

• A = Total account balance at the end of Month 2.
• P = $1,000. This is your initial investment. At the start of Month 2, there are no monthly deposits yet.
• r = 0.07
• n = 12
• t = ¹⁄₁₂

$$\textbf{A} = $1,000(1 + \frac{.07}{12})^{12*\frac{1}{12}}$$

$$\phantom{\textbf{A}} = $1,005.83$$

Next, we can find the total interest earned this month where:

• A = $1,005.83. This is the balance we calculated at the end of Month 2, before this month's deposit is added.
• P = $1,000. This is your initial investment.

$$\textbf{Interest} = $1,005.83 - $1,000$$

$$\phantom{\textbf{Interest}} = $5.83$$

By the end of Month 2, you earned $5.83 in interest on your initial investment, and also deposited $100 into your account, so your new account balance is $1,105.83!

Month 3: At the end of the third month, you earned interest on the entire balance of your account, which now includes your initial investment, a monthly deposit, and interest. Let's calculate your account balance at the end of Month 3 where:

• A = Total account balance at the end of Month 3.
• P = $1,105.83. This is your account balance at the end of Month 2.
• r = 0.07
• n = 12
• t = ¹⁄₁₂

$$\textbf{A} = $1,105.83(1 + \frac{.07}{12})^{12*\frac{1}{12}}$$

$$\phantom{\textbf{A}} = $1,112.28$$

Next, we can find the total interest earned this month where:

• A = $1,112.28. This is the total balance we calculated at the end of Month 3, before your deposit is added.
• P = $1,100. This is your initial investment and the deposit you added at the end of last month.

$$\textbf{Interest} = $1,112.28 - $1,100$$

$$\phantom{\textbf{Interest}} = $12.28$$

By the end of Month 3, you earned $12.28 in interest on your initial investment and deposit, which is more than double the amount of interest you earned the previous month! Don't forget, you also deposited another $100 into your account, which brings your new account balance at the end of Month 3 to $1,212.28!

If you keep following these steps, you can calculate your compound interest earned every month. Use the Compound Interest Calculator above to see how much compound interest you can earn over time!