finance calculator

Compound Interest Calculator

Model compound growth with deposits and time.

Formula Verified by Dr. Elizabeth Vance, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Initial amount$

Monthly contribution$

Annual return%

Years

Results

Future value

$67,358

Total contributions$46,000

Interest earned$21,358

Months invested120 months

Bookmark this Compound Interest Calculator

Compounding curves accelerate over time. Save this calculator to model savings goals under different interest rates or deposit schedules.

Formula

Compound growth with contributions

Future value = starting balance compounded monthly + each monthly contribution compounded over time

The calculator compounds the starting balance and adds each contribution month by month.

Step by step

How the calculation works

1Enter the starting balance and monthly deposit.
2Choose an expected annual return and time horizon.
3The calculator compounds growth monthly and separates contributions from earned interest.

Example

Compound interest example

Starting with $10,000 and adding $300 monthly for 10 years at 6% grows to about $64,198.

Related guides

Learn more about this calculation

Guide

Compound Interest: Formula, Examples, and Calculator

Learn how compound interest works, calculate growth with monthly deposits, compare assumptions, and avoid common projection mistakes.

Guide

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Compare simple interest and monthly compound interest, learn when each model fits, and use worked examples aligned to the calculators.

How to understand and use this calculator

The Mathematics of Compounding Growth

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods. Known mathematically as exponential growth, it stands in contrast to simple interest, where interest is earned strictly on the original principal.

The power of compounding is driven by frequency. When interest is credited to an account, it becomes part of the principal base for the next compounding period. The shorter the compounding interval (e.g., daily instead of annually), the faster your wealth accumulates.

The Compound Interest Formulas

To calculate the future value of a principal sum compounded over time, apply the standard compounding formula:

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

Where:

* $A$ is the future value of the investment, including interest.

* $P$ is the principal investment amount.

* $r$ is the annual interest rate (decimal).

* $n$ is the number of times interest is compounded per year.

* $t$ is the time the money is invested in years.

When regular monthly deposits are added to the principal, the calculator combines this formula with the future value of an ordinary annuity formula:

$$A = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$

Where $PMT$ is the monthly contribution amount. This reveals how consistent, small deposits amplify compound growth over decades.

The Impact of Compounding Frequency

Compounding frequency determines how often interest is calculated and added to your balance. The most common intervals are daily, monthly, quarterly, and annually.

Daily compounding yields the highest return because interest starts earning interest the very next day. While the difference between daily and monthly compounding may seem minor on small sums, it scales significantly over long timelines and large balances. This is why credit cards charge daily compounding on debt, while savings accounts often offer monthly or daily compounding on deposits.

The Rule of 72: A Quick Mental Shortcut

To estimate how long it takes to double your money under compound interest, use the Rule of 72. Divide 72 by your annual interest rate to find the approximate doubling period in years:

$$\text{Years to Double} \approx \frac{72}{\text{Annual Rate}}$$

For example, an investment earning a consistent 8% annual return will double in value approximately every $72 / 8 = 9\text{ years}$. This mental model highlights the accelerating curves of compound growth.

Related concepts

APY

Annual Percentage Yield: the true annual rate of return reflecting compounding effects.

Rule of 72

A mathematical shortcut to estimate the years required to double an investment.

Ordinary Annuity

A series of equal periodic payments made at the end of each period, compounding over time.

Frequently Asked Questions

What is compound interest?+

Compound interest is interest calculated on the initial principal plus the accumulated interest from previous periods. It represents earning interest on interest.

What is the formula for compound interest?+

The base formula is A = P(1 + r/n)^(nt), where A is future value, P is principal, r is annual rate, n is compounding frequency, and t is time in years.

What is the difference between simple and compound interest?+

Simple interest is calculated strictly as a percentage of the original principal. Compound interest is calculated on the principal plus all previously accumulated interest, leading to exponential growth.

What does compounding frequency mean?+

Compounding frequency is the number of times interest is calculated and added to the principal balance per year (e.g., 12 for monthly, 365 for daily).

How does daily compounding differ from monthly compounding?+

Daily compounding calculates and adds interest to the balance 365 times a year, while monthly compounding does so 12 times, resulting in slightly higher returns for daily compounding over time.

What is APY (Annual Percentage Yield)?+

APY is the real annual rate of return, taking into account the effect of compound interest. It is always higher than the nominal interest rate when compounding occurs more than once a year.

What is the Rule of 72?+

The Rule of 72 is a quick shortcut to estimate when an investment will double. Divide 72 by the annual interest rate to find the approximate doubling period in years.

Does this calculator account for inflation?+

No. The calculator models nominal growth. To adjust for inflation, subtract the estimated inflation rate (e.g., 2-3%) from your annual rate input.

How do monthly deposits affect compound growth?+

Monthly deposits add new capital to the principal base regularly, giving the compounding math a larger amount to compound each month and accelerating wealth building.

Are savings account rates simple or compound?+

Almost all bank savings accounts and CDs apply compound interest, usually compounding daily or monthly and crediting interest to your account monthly.

How to understand and use this calculator

The Mathematics of Compounding Growth

The Compound Interest Formulas

To calculate the future value of a principal sum compounded over time, apply the standard compounding formula:

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

Where:

* $A$ is the future value of the investment, including interest.

* $P$ is the principal investment amount.

* $r$ is the annual interest rate (decimal).

* $n$ is the number of times interest is compounded per year.

* $t$ is the time the money is invested in years.

When regular monthly deposits are added to the principal, the calculator combines this formula with the future value of an ordinary annuity formula:

$$A = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$

Where $PMT$ is the monthly contribution amount. This reveals how consistent, small deposits amplify compound growth over decades.

The Impact of Compounding Frequency

Compounding frequency determines how often interest is calculated and added to your balance. The most common intervals are daily, monthly, quarterly, and annually.

The Rule of 72: A Quick Mental Shortcut

To estimate how long it takes to double your money under compound interest, use the Rule of 72. Divide 72 by your annual interest rate to find the approximate doubling period in years:

$$\text{Years to Double} \approx \frac{72}{\text{Annual Rate}}$$

Related concepts

APY

Annual Percentage Yield: the true annual rate of return reflecting compounding effects.

Rule of 72

A mathematical shortcut to estimate the years required to double an investment.

Ordinary Annuity

A series of equal periodic payments made at the end of each period, compounding over time.

Frequently Asked Questions

What is compound interest?+

Compound interest is interest calculated on the initial principal plus the accumulated interest from previous periods. It represents earning interest on interest.

What is the formula for compound interest?+

The base formula is A = P(1 + r/n)^(nt), where A is future value, P is principal, r is annual rate, n is compounding frequency, and t is time in years.

What is the difference between simple and compound interest?+

What does compounding frequency mean?+

Compounding frequency is the number of times interest is calculated and added to the principal balance per year (e.g., 12 for monthly, 365 for daily).

How does daily compounding differ from monthly compounding?+

Daily compounding calculates and adds interest to the balance 365 times a year, while monthly compounding does so 12 times, resulting in slightly higher returns for daily compounding over time.

What is APY (Annual Percentage Yield)?+

APY is the real annual rate of return, taking into account the effect of compound interest. It is always higher than the nominal interest rate when compounding occurs more than once a year.

What is the Rule of 72?+

The Rule of 72 is a quick shortcut to estimate when an investment will double. Divide 72 by the annual interest rate to find the approximate doubling period in years.

Does this calculator account for inflation?+

No. The calculator models nominal growth. To adjust for inflation, subtract the estimated inflation rate (e.g., 2-3%) from your annual rate input.

How do monthly deposits affect compound growth?+

Monthly deposits add new capital to the principal base regularly, giving the compounding math a larger amount to compound each month and accelerating wealth building.

Are savings account rates simple or compound?+

Almost all bank savings accounts and CDs apply compound interest, usually compounding daily or monthly and crediting interest to your account monthly.

Compound Interest Calculator

Inputs

Results

Bookmark this Compound Interest Calculator

Compound growth with contributions

How the calculation works

Compound interest example

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Compound Interest Calculator

Inputs

Results

Bookmark this Compound Interest Calculator

Key output metrics

Contributions vs interest

Compound growth timeline

How to understand and use this calculator

The Mathematics of Compounding Growth

The Compound Interest Formulas

The Impact of Compounding Frequency

The Rule of 72: A Quick Mental Shortcut

Related concepts

Frequently Asked Questions

Compound growth with contributions

How the calculation works

Compound interest example

Learn more about this calculation

Compound Interest: Formula, Examples, and Calculator

Simple vs Compound Interest: Linear Growth vs Interest on Interest

Key output metrics

Contributions vs interest

Compound growth timeline

How to understand and use this calculator

The Mathematics of Compounding Growth

The Compound Interest Formulas

The Impact of Compounding Frequency

The Rule of 72: A Quick Mental Shortcut

Related concepts

Frequently Asked Questions