On this page is a detailed *compound interest calculator*, along with the *compound interest formula*. The calculator allows you to calculate compound interest from a starting lump sum, periodic additions, and for annual, monthly, and daily compounding periods. Finally, our calculator will graph the growth of the investment over time and report a final amount.

## Compound Interest Calculator

### Using the Compound Interest Calculator

**Investment Starting Amount –**The lump sum at the beginning of the compounding period. If you are modeling your portfolio, you should use “today’s value”.**Periodic Investment Amount**– The amount, in dollars, you add on a periodic basis.**Periodic Addition Frequency**– How often you add the above amount to your portfolio.**Interest Rate**– APR – The annual percentage rate the investment pays every year (quoted as APR if it is a bank account or similar)**Periods to Compound**– The number of periods (the type is selected below) that the starting amount and the periodic additions will compound.**Type of Periods**– How often the interest is applied… this field also affects the number of periods field set above (so if you select ‘Daily’, make sure you enter the number of days to compound above).

## Compound Interest and Your Portfolio

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” – Albert Einstein

Compound interest is a powerful concept which is fully worth grasping completely while learning more about your investment portfolio. At its heart: the money in your account earns interest, but the interest itself * also* earns interest – eventually snowballing into a larger and larger base on which to earn interest.

The exact same concept applies when discussing * dividends*… a topic that we’ve visited quite often here on DQYDJ. This site’s initial success was due to our dividend reinvestment return calculators, which vividly illustrate the effect of reinvesting dividends on stock returns. Over a 40 year career, dividends and interest paid on previous dividend-purchased-shares or previous interest can add up to a sizeable chunk of your portfolio’s final value.

## The Compound Interest Formula

The compound interest formula is simple:

P * ( 1 + (i / n) ) ^ (n*t)

Where:

- P is the principal, or starting amount
- i is the interest rate, APR
- n is how many times per year the sum is compounded
- t is the number of years to run the calculation

Let’s work through a scenario now using the compound interest calculator and the compound interest formula:

Starting with $1,000, how much money would you have if you put your money into a savings account with a 5.5% APR, compounded daily, for 5 years?

A naive calculation would say: $1,000 * 5.5% = $55 a year, multiply that by 5 and you get $275 for a total of

$1,275after 5 years.You know from my use of the word ‘naive’ that’s incorrect. Plugging the numbers into the calculator, you get

$1,316.50– compound interest made a noticeable difference in the calculation.Let’s see how we got that – plugging the numbers in the compound interest formula, we get:

1000 * (1 + (.055 / 365) ) ^ (365 * 5) =

1000 * (1 + (.0015068…) ) ^ (1,825) =

1000 * 1.3165034… =

$1,316.50

And there you go – without a feel for compound interest, somebody could spirit away $41.50 with you none the wiser!

## The Effect of Compounding Frequency on Interest

One of the variables we noted in the compound interest calculation was the idea of the *compounding frequency*. Think of the compounding frequency as how often the compounding works on itself (compounding on compounding – it’s all compounding all the way down!). **Daily compounding** means the rate is applied to the balance at the end of every day, and likewise for other forms of compounding, such as weekly, monthly or annual. There is also the idea of ‘continuous’ compounding, where the compounding is always happenings on an * instantaneous* sum of money.

The best way to get a sense of how the different compounding period affect the balance in an account, it’s easiest to take a look at a graph. Wikipedia had a nice illustration from user Jelson25 which we reproduce here:

As you can see, compound interest is a simple topic to get a reasonable grasp on, even though it might introduce a lot of details throwing you off the main topic. In the end it boils down to one simple fact: interest also works upon previous interest. Whether this helps you or hurt you depends on what side of the transaction you’re on – but heed Albert Einsteins advice, understand it, and profit from it as much as you can.

For some other calculators and articles in our investment basics series, please try:

- Present Value Calculator (with the Present Value Formula)
- Compound Annual Growth Rate Calculator (with the CAGR formula)

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