# How To Calculate Compound Interest

Whoever came up with the phrase, “It takes money to make money,” was probably a big fan of compound interest.

One of the most powerful forces in finance, compound interest can multiply your money. And the longer you’re earning compound interest, the more your money will multiply.

In this article, I’ll point you to a compound interest calculator, give you the compound interest formula and show you how just a little money can turn into \$1 million via compound interest, given enough time.

## What Is Compound Interest?

Compound interest is calculated on the initial principal plus the interest that you’ve earned during previous periods. In other words, it allows you to earn interest on your interest.

Investing early and giving your money time to compound itself is a huge advantage when it comes to saving for retirement.

## How Does Compound Interest Work?

Four variables determine how much money you’ll make with compound interest:

• Interest rate. In the case of a fixed-interest loan or a certificate of deposit (CD), you’ll know what the interest rate is going to be upfront. However, the “interest,” or your return on investment (ROI), will vary wildly in the stock market, though it’s more predictable over decades. Even your bank will occasionally change its savings account interest rate.
• Length of time. With compound interest, the time you allow your money to accrue interest matters a great deal. You can invest or save much less money than someone else and end up with more — simply by giving it more time to grow.
• Compounding period. This is the amount of time that passes between when your interest gets calculated and when it gets calculated again. The compounding period can be continuous, daily, weekly, monthly, quarterly, semi-annually or annually.
• Deposits. You can always add additional money. In fact, money expert Clark Howard would like you to increase the amount you’re saving and investing over time.

## Compound Interest vs. Simple Interest

With simple interest, the interest rate applies only to your initial principal. In other words, you don’t earn interest on your interest.

Compound interest vs. simple interest helps illustrate “the miracle of compounding interest,” as some call it.

Let’s assume that you and your friend Merckle each have \$100. Each of your accounts earns 10% interest that’s calculated annually. But you get compound interest and Merckle gets simple interest. How will each of you do after five years?

YouMerckle
Year 1\$110\$110
Year 2\$121\$120
Year 3\$133.10\$130
Year 4\$146.41\$140
Year 5\$161.05\$150

As you can see, your return will outpace Merckle by \$11.05: more than 11%. You can imagine how big of a difference compound interest can make with a large amount of money and much more time.

## Compound Interest Calculator

As I will show shortly, the formula for calculating compound interest is involved enough that you probably won’t want to do it by hand. Luckily, you can use a compound interest calculator to do the math for you.

Investor.gov puts out a nice compound interest calculator. Personally, I like to use this one.

Using a compound interest calculator can be especially useful when you’re trying to figure out the potential range of outcomes. For example, if you’re invested in an S&P 500 index fund and you plan to be in it for the next 20 years, you can quickly calculate how much you’ll have if you get 5% or 10% annual return (“interest”).

### Compound Interest Formula

The compound interest formula is as follows:

A = P(1+r/n)^nt

Here are the elements of this formula defined:

A: Final amount of money
P: Initial Principal
R: APY (interest rate)
N: Compounding periods per year
T: Number of years

## How To Get to \$1 Million via Compound Interest

I’ve already talked about the power of compound interest, especially over long time periods, and you’ve probably seen charts that illustrate compound interest in eye-popping ways.

Here’s a new one.

Let’s assume you invest in a total stock market index fund that earns a modest 7% annual return. You invest the same amount of money in it each month.

Depending on your monthly investment, how long will it take you to become a millionaire?

Monthly ContributionsTime To \$1 Million
\$50/month70.5 years
\$10060.5
\$25047.5
\$50038
\$1,00028.5
\$2,50018
\$5,00012
\$10,0007

Let’s take a look at one final example that illustrates how important it is to start saving and investing as early in life as you possibly can, even if it’s only a small amount.

Eunice is a 22-year-old recent nursing school graduate. She doesn’t have much extra income, but she’s determined to take advantage of compound interest and start saving for retirement now.

Brad is a 40-year-old party animal who hasn’t saved a dollar for retirement. Lucky for Brad, he’s a middle manager at a corporate conglomerate in the auto industry and makes a good salary. He figures he’ll be fine. He’s got time, after all.

They both plan to retire at 65. They want \$1 million in total stock market index fund when they retire. Eunice has 43 years to save, while Brad has 25.

How much will they each have to contribute to the index fund to reach their goal, assuming a 7% annual return?

NameWeekly ContributionsMonthly ContributionsYearly Contributions
Eunice\$77.62\$336.73\$4,036

Eunice has about 1.7 times as much time as Brad, but Brad has to invest 3.9 times as much as Eunice each week. The chasm between those numbers would only grow if Eunice started earlier or Brad started later.

You can’t turn back time or change your age. But you can understand how important it is to start contributing to your retirement as early as you can.

## Final Thoughts

Saving and investing is crucial when it comes to funding your retirement or even building wealth.

Compound interest is especially powerful over long periods of time.