Financial Calculators
Compound Interest Calculator

# Compound Interest Calculator

Compound interest calculator that uses the interest formula (A = P(1 + r/n)ⁿᵗ) to help users understand the impacts of compound interest and money growth over time.

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## Scope of Application

Compound interest is an important concept to understand that is widely used in investing, finance, and banking. Compound interest is defined as the interest earned on a loan or investment that comes from both the initial principal and the accumulated interest.

## Example

John invests $1,000 in a bond with a growth rate of 10%. After the first year, John will earn$100 in interest (10% of the initial investment of $1,000). Now, John has$1,100. Another year goes by, and John collects the 10% interest again. Since his balance is now $1,100, the interest earned will be$110 (10% of the $1,100). John’s balance at the end of the second year is now$1,210.

As you can see, the interest earned in the example above will continue to grow each year. That’s the power of compounding! The longer John keeps his money invested, the faster it will grow.

## Understanding the Basic Compound Interest Formula

The best part about this calculator is that you don’t have to worry about knowing the underlying formulas for how to calculate compound interest. However, we’ll break it down so you have a good understanding of how the calculator works.

The formula to calculate compound interest is:

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

• A = Final balance (including initial amount plus all accumulated interest)
• P = Principal or initial investment
• r = Interest rate
• n = The frequency of compounding (weekly, monthly, yearly, etc.)
• t = The amount of time the amount will accumulate interest

## Alternate Calculations

While most people will use the default formula to calculate the expected result of compound interest, several other formulas are available. Each formula has its use and purpose. You can select the desired formula under the calculate field.

## Principal (P) using A

This option uses the total ending balance to work backward to find the initial principal amount using the formula:

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

## Rate (r)

In some cases, you may be exploring a few different investment options. Use the formula:

$$r = n\left[\left(\frac{A}{P}\right)^{\frac{1}{nt}} - 1\right]$$

This formula will show you what interest rate is needed to reach a particular final goal. If you plan to get $15,000 in 10 years, you need to know how much interest you will need to earn if you invest$5,000. In this example, the calculator will show you that (compounded monthly), you will need to find an investment that earns at least 11% per year.

## Time (t)

Compound interest is most potent when you let your money earn interest for a long time. This option will help you understand how long it will take for your investment to reach a certain balance. Suppose you want to retire with $1,000,000. In that case, it will take about 30 years with an initial investment of$25,000 and an interest rate of 10% (compounded monthly). If 30 years is too long, you can use this information to decide to increase your initial investment or find another investment that has a higher interest rate.

## Using the calculator

Using our compound interest calculator is simple. Before you get started, you need to decide what you are trying to calculate (final balance, interest rate, etc.). This will help you select the right formula from the Calculate field.

• Step 1: Select the desired formula (Total P+I (A), Principle (P) using I, etc.).
• Step 2: Each formula will require different inputs. Enter the requested information in the fields. Note: All fields must be filled to calculate the answer. Once all fields are entered, click the Calculate button.
• Step 3: Review the results. The most important information is the final calculation results. However, our calculator also shows how the answer was calculated and displays detailed steps so you can follow along.
• Step 4: Run another calculation. Perhaps you want to calculate how the results would look with different criteria. Change the information above and hit the Calculate button again.

## Real Example

Let’s say you have $10,000 to invest, and you want to know how long it will take to grow to$100,000. You’ve selected an index fund that you believe will grow at 8% each year.

Start by selecting the Time (t) option in the calculate field. This will change the form to show the following fields: Total P+I (A), Principal (P), Annual Rate (r), and Compound (n).

Next, enter the following values:

• Total P+I (A): $100,000 • Principal (P):$10,000
• Annual Rate (r): 8%
• Compound (n): For the sake of this exercise, we’ll assume the amount is compounded annually.

Once you hit the Calculate button, you’ll see that it will take 29.919 years to reach your goal.

## Key Benefits and Helpful Tips

Having a good understanding of how compound interest works can significantly improve your effectiveness in financial planning. This compound interest calculator can help you set goals and ensure you are on the right track.

### Key Benefits:

• No Memorizing Formulas - There are hundreds of different formulas in mathematics and finance. This calculator helps you solve a relatively complex calculation without memorizing or looking up the compound interest formula.
• Detailed Explanation - Most online calculators give you the answer. While this is beneficial, it’s good also to see how the results were calculated in a step-by-step breakdown. This is especially useful for students trying to understand the formula itself.
• Opportunities for experimentation - Our compound interest calculator allows you to run quickly several scenarios to help you decide on your finances.