How to Calculate Compound Interest

Whoever coined 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 earn compound interest, the more your money will multiply.

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


Contents


What is compound interest?

Compound interest is calculated on the original principal plus the interest you have earned in previous periods. In other words, it allows you to earn interest on your interest.

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


How does compound interest work?

Four variables determine how much money you will earn with compound interest:

  • Interest rate. In the case of a fixed rate loan or a certificate of deposit (CD), you will know in advance what the interest rate will be. However, “interest,” or your return on investment (ROI), will vary wildly in the stock market, although it is more predictable over decades. Even your bank will occasionally change the interest rate on their savings account.
  • A length of time. With compound interest, when you let your money earn interest is very important. You can invest or save a lot less money than someone else and end up with more – simply by giving them more time to grow.
  • Capitalization period. This is the time that elapses between when your interest is calculated and when it is recalculated. The capitalization period can be continuous, daily, weekly, monthly, quarterly, half-yearly or annually.
  • Deposits. You can always add extra money. In fact, financial expert Clark Howard would like you to increase the amount you save and invest over time.

Compound interest vs simple interest

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

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

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

You Merck
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 exceed Merckle by $11.05: over 11%. You can imagine how much difference compound interest can make with a lot of money and a lot more time.


Compound Interest Calculator

As I’ll show shortly, the formula for calculating compound interest is complicated enough that you probably don’t want to do it by hand. Fortunately, you can use a compound interest calculator to do the math for you.

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

Using a compound interest calculator can be particularly helpful when trying to determine the potential range of results. For example, if you’ve invested in an S&P 500 index fund and plan to stay there for the next 20 years, you can quickly calculate how much you’ll get if you earn a 5% or 10% annual return (“interest rate”). ”).

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
P: initial principal
A: APY (interest rate)
N: Capitalization periods per year
T: Number of years


How to reach $1 million via compound interest

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

Here’s a new one.

Say you invest in a total stock market index fund that generates a modest 7% annual return. You invest the same amount of money in it each month.

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

Monthly contributions Million Dollar Time
$50/month 70.5 years
$100 60.5
$250 47.5
$500 38
$1,000 28.5
$2,500 18
$5,000 12
$10,000 seven

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

Eunice is a 22 year old 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 boy who hasn’t saved a dollar for his retirement. Fortunately for Brad, he is a middle manager in a conglomerate of companies in the automotive industry and earns a good salary. He thinks he will be fine. He has time, after all.

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

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

Last name Weekly contributions Monthly contributions Annual dues
Eunice $77.62 $336.73 $4,036
Brad $304.06 $1,317.38 $15,811

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

You cannot go back in time or change your age. But you can understand how important it is to start contributing to your retirement as soon as possible.


Final Thoughts

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

Compound interest is especially powerful over long periods of time.

If you invest, you will not be able to predict what your return on investment will be from one year to the next. But if you stay invested in low-cost index funds for decades, you can almost certainly expect a good annual return that puts compound interest to work funding your retirement.


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