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Compound Interest Calculator

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The initial capital is the amount you will invest or lend at the beginning of the period.
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The interest rate is the percentage that will be applied to the initial capital during the period. It can be monthly or yearly.
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The period is the duration of the investment or loan, in months or years, depending on the selected interest rate.
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The monthly contribution is the amount you add to the initial capital each month during the investment or loan period.
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How to Use the Compound Interest Calculator

To use the Compound Interest Calculator, follow the steps below:

  1. Enter the initial capital you want to invest or lend in the Initial Capital ($) field.
  2. Enter the interest rate in the Interest Rate (%) field and select whether it is monthly or yearly.
  3. Set the investment or loan period in the Period (t) field and choose whether it is in months or years.
  4. If desired, enter a monthly contribution in the Monthly Contribution ($) field.
  5. Click the Calculate Compound Interest button to see the detailed results of your investment.

The calculator will provide an investment summary, including the total invested, total interest earned, and the final amount, along with illustrative graphs.

Example of Compound Interest Calculation

Suppose you invest $ 1,000.00 with an annual interest rate of 12% for a period of 2 years, making a monthly contribution of $ 100.00.

Example of compound interest calculation

By entering these values into the calculator and clicking Calculate Compound Interest, you will see the investment summary and corresponding graphs, allowing you to clearly visualize how your investment grows over time thanks to compound interest and monthly contributions. As shown in the image below:

Example of compound interest calculation result

This example demonstrates how compound interest can significantly increase the value of your investment over time, especially with regular contributions.

What is Compound Interest?

Compound interest calculates earnings on the principal plus accumulated interest, creating the "interest on interest" effect that drives growth over time.

Quick example: investing $ 100.00 at 10% per year, you end the first year with $ 110.00. In the second year, interest is applied to $ 110.00 and generates $ 11.00, closing the period with $ 121.00.

This mechanism is ubiquitous in investments, loans, and financing, as it better reflects the real growth of capital than simple interest. For long cycles, the compound effect stands out and brings considerably higher returns.

Need to compare with simple interest? Visit simple interest calculator to see the results.

Difference Between Simple and Compound Interest

Simple interest always targets only the initial capital. Compound interest accumulates each gain and reinvests it, growing at an accelerated pace each period.

Comparing: with 10% per year, simple interest yields $ 10.00 every year. With compound interest, the first month will yield the same amount as simple interest ($ 10.00), however, in the second month, the interest will already be applied to a higher amount ($ 110.00), so it will yield more ($ 11.00).

Although the difference seems small at the beginning, over time compound interest significantly outperforms simple interest. With our example, in the third year you would already have $ 133.10 with compound interest, while simple interest would yield only $ 30.00 in total. If we continue this example for 10 years, simple interest would give $ 100.00, while compound interest would result in $ 259.37.

Compound Interest Formulas

There are two main expressions: one for growth with only the initial capital and another that includes recurring deposits.

Compound Interest Amount Formula without Contributions

When you invest only the initial capital, the formula is:

M=C×(1+i)t\mathbf{\mathbf{M = C \times (1 + i)^{t}}}
M Final amount (capital + interest).
C Initial capital.
i Interest rate per period.
t Number of periods.

Compound Interest Amount Formula with Contributions

Adding constant contributions (PMT), the amount follows:

M=C×(1+i)t+PMT×(1+i)t−1i\mathbf{\mathbf{M = C \times (1 + i)^{t} + PMT \times \frac{(1 + i)^{t} - 1}{i}}}
PMT Value of the periodic contribution.

Interest is always calculated as the final amount minus the total invested (initial capital + sum of contributions). Therefore:

J=M−(C+PMT×t)\mathbf{\mathbf{J = M - (C + PMT \times t)}}

FAQ

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01. What are compound interest and how do they work in practice?

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02. Is it possible to simulate scenarios with monthly contributions in the compound interest calculator?

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03. Where are compound interest applied in the financial market?

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