How Does Compound Interest Work? - Humbled Budget (2024)

Table of Contents

Introduction

Compound interest is the most powerful component in the universe. It’s so important that Albert Einstein called it “the greatest mathematical discovery of all time.”

What does this mean for you? If you start investing young, compound interest will grow your money faster than simple interest, which means you’ll have more money to spend or save later.

What Is Compound Interest?

Compound interest is the magic that allows your money to work for you. It doesn’t mean you’ll be able to retire by 30 or buy a Lamborghini (though you can use compound interest to get closer).

It does mean that if you invest wisely, your savings will grow faster than they would otherwise and there’s nothing more powerful than watching your savings grow into something bigger and better.

Compound interest happens when the good in your principal grows as time passes. If you put $100 in a savings account that pays 5% simple annual interest, at the end of year 1, you’d have $105 in your account: $100 + ($100 x .05).

Instead of getting paid simple annual interest at 5%, the bank paid compound yearly interest at 5% per year, then after one year, there would be $107 in the account: ($100 + [$100 x .05]) x 1/2 = $107.

Compound Interest Calculator

It is beneficial to have a compound interest calculator on hand for many reasons. First, if you have an investment or money saved up and want to know how much money you will have at a given time in the future, this can be helpful.

Second, if you want to know how long it will take for your investment or savings to double, then this can also be helpful.

Third, if you want to calculate how much interest per year or month is being earned on an account with compound interest rates applied (this type of calculation requires using both the annual percentage rate [APR] and continuously compounded rate), then having access to such a tool would make things easier for users who do not like doing math manually.

How Is Your Money Safe in a Bank?

A bank is a place where people deposit money and get loans. It holds your money in trust, so you can’t spend it, but it will allow you to borrow some of it back.

Banks offer different types of accounts and products. You can keep your money as savings (which earns interest) or use it to make purchases on a credit card (which doesn’t deserve any interest).

Suppose you have enough money in an account. In that case, the bank will let you borrow some of that money for a fee: this is called overdraft protection because if all the funds aren’t available at once, then they’ll lend them from somewhere else so that there’s always enough cash on hand even if someone wants more than what’s available right now.

There are also fees for withdrawing from an ATM and having checks written on behalf of another person (called check processing), which may be required when paying rent or utility bills online through an automated system such as Chase WebPay or PayNearMe.

How Does Compound Interest Work? - Humbled Budget (1)

How Interest Rates Affect Investments

The interest rate you receive is also the nominal interest rate. The return on investment (ROI) is often calculated using this number, but there are other ways to figure it out.

This is because the nominal interest rate doesn’t tell you how much money will remain in your account at the end of a period. It’s just an estimate based on what you might earn if you kept all your money invested at that same rate over time.

For example, if an investment paid 4% annual interest, but inflation was 3%. After one full year, your investment would be worth $4*(1+0.03)-1 = $3.97 more than when it started but only if it was never spent on anything besides buying more shares in that 4% stock.

If, instead, we invested our initial $100 into, say, ten different stocks and bonds are earning 4% each. After one year, we’d have roughly ($100*0.04)^10 = approximate $3 more than before, thanks to compound interest (though this amount could vary depending on which investments had higher growth rates).

To calculate gross or net interest rates, we must first determine whether taxes have already been applied by comparing gross vs net values found somewhere like the US Treasury Department website.”

The Example of the Wealthiest Man in America

The story of Andrew Carnegie is a perfect example of how compound interest works. In his early 20s, Carnegie worked as a telegrapher for Western Union and saved $500 from his salary.

He invested this money in stocks and bonds, which earned him enough to buy out his boss for $2,500, but then he sold them for $5,000. This initial investment grew at an annualized rate of 7%, meaning that by the end of Carnegie’s life, it was worth over $6 billion in today’s dollars!

The best way to illustrate how this happened is through math. If your savings grow at an annualized rate of 10% each year (which is close to what most banks aim for), after five years, your initial investment will be worth more than double what it was initially.

The following year it will double again; by year 10, it will have grown almost 900 times bigger than when you started.

Investing can be scary if you don’t know where to start or where your money should go, but thankfully there are plenty of online tools that make things easier. Please take a look at our compound interest calculator.

How Does Compound Interest Work? - Humbled Budget (2)

You have a better chance of growing your wealth by investing

Compound interest is the difference between investing and saving. For example, suppose you earn 10% on an investment that pays no dividends or interest.

You invest $100, and at the end of 1 year, you have $110. You could have just saved your money in a savings account instead, which would also be paying 10% interest (after taxes).

Thus, if you had kept your original $100 in a savings account without investing it, you would now have $110 after one year.

However, things start to change dramatically when we look at compound interest over more extended periods.

To illustrate this point, let’s imagine that instead of saving your money for one year (without earning any interest), we invest it for 30 years (so now our initial investment has become about 300 times larger).

If both investments earned 10% annually, then after 30 years, our savings would have grown from 100 dollars to 3200 dollars – which isn’t bad.

Now, let’s compare this amount with what our original investment would be worth if we invested instead: After 30 years, that same initial amount will grow into an impressive 958,876 dollars.

Conclusion

The secret behind achieving your financial goals is using compound interest’s power. The basic idea is that you can make more money by investing and earning returns on those investments over time than you would by simply saving.

Most people don’t realize how much they could benefit from this approach until they learn about it firsthand, and even then, many still don’t take action because they think it sounds too complex or complicated.

Here’s what we know: if you want to achieve financial freedom sooner rather than later, you need to start taking steps toward making it happen.

How Does Compound Interest Work? - Humbled Budget (2024)

FAQs

Is compound interest a good way to budget money? ›

The idea of compound interest (as compared to simple interest) is fundamental to investing because it can ultimately lead to a greater return in your account.

How does compound interest work with funds? ›

Compound interest is what happens when the interest you earn on savings begins to earn interest on itself. As interest grows, it begins accumulating more rapidly and builds at an exponential pace.

How much is $1000 worth at the end of 2 years if the interest rate of 6% is compounded daily? ›

Hence, if a two-year savings account containing $1,000 pays a 6% interest rate compounded daily, it will grow to $1,127.49 at the end of two years.

How does compound interest work Dave Ramsey? ›

After a period of time, with the principal (the original chunk of money you put in) and the interest that your money earned, you end up with a larger total amount than you started with. And if you leave the money alone, you'll earn interest based on that new, larger total—that's called compound interest.

Does paying $1 a day stop compound interest? ›

So what about paying daily? Paying more frequently, such as weekly or daily, won't make any difference unless you're paying more. There's no magic trick to stopping compound interest. The following graph shows what an extra $1 a day would achieve with our hypothetical $500,000 loan.

What is the 50 30 20 rule of money? ›

The 50/30/20 budget rule states that you should spend up to 50% of your after-tax income on needs and obligations that you must have or must do. The remaining half should be split between savings and debt repayment (20%) and everything else that you might want (30%).

What is the miracle of compound interest? ›

Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid. Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”

What is the magic of compound interest? ›

In other words, compound interest involves earning, or owing, interest on your interest. The power of compounding helps a sum of money grow faster than if just simple interest were calculated on the principal alone. And the greater the number of compounding periods, the greater the compound interest growth will be.

How long will it take $4000 to grow to $9000 if it is invested at 7% compounded monthly? ›

Substituting the given values, we have: 9000 = 4000(1 + 0.06/4)^(4t). Solving for t gives us t ≈ 6.81 years. Therefore, it will take approximately 6.76 years to grow from $4,000 to $9,000 at a 7% interest rate compounded monthly, and approximately 6.81 years at a 6% interest rate compounded quarterly.

What will $1 000 be worth in 20 years? ›

As you will see, the future value of $1,000 over 20 years can range from $1,485.95 to $190,049.64.
Discount RatePresent ValueFuture Value
6%$1,000$3,207.14
7%$1,000$3,869.68
8%$1,000$4,660.96
9%$1,000$5,604.41
25 more rows

What is $5000 invested for 10 years at 10 percent compounded annually? ›

The future value of the investment is $12,968.71. It is the accumulated value of investing $5,000 for 10 years at a rate of 10% compound interest.

Do 90% of millionaires make over $100,000 a year? ›

Only 31% averaged $100,000 a year over the course of their career,” the study found, “and one-third never made six figures in any single working year of their career.” Just look at the story of former custodian Ronald Read for a perfect example.

How to be a millionaire in 10 years? ›

Now, let's consider how our calculations change if the time horizon is 10 years. If you are starting from scratch, you will need to invest about $4,757 at the end of every month for 10 years. Suppose you already have $100,000. Then you will only need $3,390 at the end of every month to become a millionaire in 10 years.

What is compound interest Warren Buffett? ›

Compound interest describes the ability to earn not only interest on the principle but also reinvested interest on the interest. “ We started at a very early age in rolling the snowball down,” Buffett said in 1999. “ The trick is to have a very long hill, which means either starting very young or living ...

Is compound interest really that good? ›

A simple definition. Compound interest makes your money grow faster because interest is calculated on the accumulated interest over time as well as on your original principal. Compounding can create a snowball effect, as the original investments plus the income earned from those investments grow together.

Is compound interest a good thing? ›

Why is compound interest important? Compound interest causes your wealth to grow faster. It makes a sum of money grow at a faster rate than simple interest because you will earn returns on the money you invest, as well as on returns at the end of every compounding period.

What are the disadvantages of compound interest? ›

Disadvantages Explained

Works against consumers making minimum payments on high-interest loans or credit card debts: If you only pay the minimum, your balance could continue growing exponentially as a result of compounding interest.

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