How Compound Interest Works, Explained: 7 Things to Know

Intro

On average, 42% of adults solved an international survey's compound interest question. How compound interest works, explained: seven things to know, each with what it is, its first step, and its limit. Try it: $100 at 2% a year, left untouched for five years. More than, exactly, or less than 110?

The answer is in number one. Every number comes from official pages linked below. Henry only points at what they show. Number one: what compounding is, and the answer to that question.

1. What compounding is

What it is: interest is the price people pay for the use of someone else's money, a central bank's video lesson explains. A markets regulator's glossary defines compound interest as interest paid on principal and on accumulated interest. The principal, the lesson adds, is the amount you initially deposit. How it works: money put into a bank account is lent to the bank, the lesson explains, so the bank must pay you.

Official savings rules describe interest as a payment for the use of funds, figured by applying a periodic rate to the balance. Once interest is added to the balance, the next interest is figured on that larger balance. Now the survey's answer: after one year, the account holds $102. After five years, it holds more than 110, because each year's interest also earns interest.

On average across participating countries and economies, 42% of adults in that survey got it right. The first step, from the regulator's official compound interest calculator: step one asks for your initial investment. Its label explains: the amount of money that you have available to invest initially. What it takes: an account or investment that pays interest, and, in the lesson's words, self-discipline.

Its limit: because a bank deposit carries little risk, the lesson says, the interest rate it pays is relatively low. Higher risk means higher potential rewards, it adds, but also higher potential for loss. Deposit protection and taxes on interest differ from place to place, so check the rules where you live. Quick check for number one: know your principal, your rate, and whether interest is added to the balance.

Subscribe, because number two shows the extra twenty-five cents where compounding begins. Number two puts that rule into $100 and two years.

2. Interest on interest

Number two: interest on interest, the part that makes compounding grow. What it is, in the regulator's words: compound interest is the interest you earn on interest. A central bank's wealth guide agrees: interest is paid on previously earned interest as well as on the original deposit. How it works, with the regulator's example: $100 that earns 5% interest each year.

At the end of the first year, there are $105. At the end of the second year, $110 and twenty-five cents. $5 came from the first hundred, and twenty-five cents from the first year's interest. Each new year's interest is figured on the whole balance: the deposit plus all earlier interest.

Those twenty-five cents may not sound like much, the page says, but they add up over time. Another page of the same regulator adds that over time, even a small amount saved can add up to big money. The first step, in a central bank's lesson: putting savings in an interest-bearing account and leaving them there. For term deposits that compound, official savings rules require a statement that a withdrawal of interest will reduce earnings.

What it takes: patience, and, the lesson adds, regular contributions on top of what is already growing. It suggests paying yourself first, with money directly deposited from each paycheck. Its limit: 5% is the page's example rate, not a promise of what any account will pay. Rates, taxes on interest, and account rules differ from place to place, so check the rules where you live.

Quick check for number two: an interest-bearing account, interest left inside, and regular contributions. Number three shows what that same $100 becomes with enough time.

3. The role of time

Number three: time, the ingredient that lets interest build on interest for longer. What it is, in a central bank's guide: compounding has a greater effect over a longer period. Back to the regulator's $100 at 5%, with nothing ever added. In ten years, the page says, it grows to more than $162.

In twenty-five years, almost $340, from the same single hundred. How it works: the longer interest stays in, the larger the balance that each new year's interest is figured on. The guide offers a quick estimate called the Rule of seventy-two. Divide seventy-two by the expected rate of return to find roughly how many years money takes to double.

Its example: $5,000 at 8%, and seventy-two divided by eight is nine. So about 10,000 in nine years, about 20,000 in eighteen, and 40,000 in twenty-seven. The first step, from a central bank's lesson: it is not just how much you save, but when you start. The lesson sums it up in its own words: start early and save often.

What it takes: years, and the official calculator asks for them under length of time in years. Its limit: the Rule of seventy-two gives only an estimate. 8% is the guide's example, not a promise. The guide adds that, generally, the higher the expected return, the higher the risk of losing money.

Accounts used for long-term saving, and their tax rules, differ from place to place, so check where you live. Quick check for number three: when you start, how often you save, and the Rule of seventy-two estimate. Number four looks inside each year: how often the interest is added.

4. How often it compounds

Number four: how often interest compounds, from once a year to every day. What it is: the regulator's calculator offers annually, semiannually, quarterly, monthly, and daily. Its label for that box reads: times per year that interest will be compounded. How it works: each time interest is compounded, it joins the balance, and the next interest is figured on a larger balance.

Official savings rules say the total interest paid depends on the interest rate and the frequency of compounding. Their worked example uses a rate of 5.25%, compounded daily, on $1,000. Over one year, that deposit earns $53 and ninety cents in interest. Daily compounding means each day's interest can begin earning interest the very next day.

The first step, from those rules: account disclosures must state how often interest is compounded and credited. The rules also say a bank must provide account disclosures to a consumer upon request. In the official calculator, that answer goes into step four, which the page calls compound it. What it takes: reading two lines of the account terms, how often interest compounds and how often it is credited.

The rules also require an explanation of how the balance that earns interest is computed. Its limit: the regulation's calculation assumes all principal and interest remain on deposit, with no withdrawals during the term. Some term deposits pay interest out instead of compounding it, so the rules let their yield equal their rate. Compounding rules, disclosures, and deposit protection differ from place to place, so check the rules where you live.

Quick check for number four: how often interest compounds, how often it is credited, and how the balance is figured. Number five turns all of that into one number you can compare: the annual percentage yield.

5. The rate and the APY

Number five: the interest rate and the annual percentage yield, two figures for the same account. What it is: official savings rules define the interest rate as the annual rate that does not reflect compounding. The annual percentage yield, or APY, reflects the total interest paid, based on the rate and how often it compounds. In the rules' example, the rate is 5.25%, and the APY is 5.39%.

How it works: the yield is the interest earned in a year, divided by the deposit, shown as a percentage. $53 and ninety cents on 1,000 works out to 5.39%. A banking regulator's help page notes that each bank generally sets its own interest rates on savings accounts. Under those savings rules, an advertisement that states a rate of return must state it as an annual percentage yield.

The first step, from those rules: account disclosures must show both the annual percentage yield and the interest rate. The help page also points to an official APY tool that can assist in verifying an account's yield. What it takes: the two figures, and the minimum balance needed to obtain the advertised yield. For investments, the rate is only an estimate: the calculator calls it your estimated annual interest rate.

It also offers a variance range, showing results for rates above and below yours. Its limit: those rules also require a statement that fees could reduce the earnings on the account. Disclosure rules and taxes on interest differ from place to place, so check where you live. Quick check for number five: compare APYs, note the rate beside each one, and check the balance needed.

Number six is the same math pointed the other way: compounding on what you owe.

6. Compounding on debt

Number six: compounding on debt, the side of compound interest that you pay. What it is, in a central bank's wealth guide: there is a flip side to compound interest, interest you are charged. The guide says this compound interest is charged for purchases on your credit card. When you borrow, a central bank's video lesson notes, you are paying to use someone else's money.

How it works: when a card balance is not paid off monthly, the guide says, you pay interest on everything purchased. It is the same engine as number two, now working on a balance that is owed. A markets regulator's page says most credit cards charge high interest rates if the balance is not paid in full each month. It adds that eliminating high-interest debt pays off better, and with less risk, than any investment strategy.

The first step, in the guide's own example: listing the balance, interest rate, and monthly interest on each card. The regulator's page sets the order: first pay down the card that charges the highest rate. It says to pay as much as possible on that one, while still paying the minimum on the others. What it takes: knowing what you owe.

The page suggests tracking spending every time you use a card. Before borrowing, the guide lists what to learn: the interest rate, the annual percentage rate, finance charges, fees, and penalties. Its limit: the guide calls this the compound interest you pay, not the kind that builds wealth. Card rates, fees, and borrowing rules differ from place to place, so check the rules where you live.

Quick check for number six: each card's balance, interest rate, and monthly interest listed. Number seven is easy to miss, yet it typically comes with investing: fees.

7. Fees and compounding

Number seven: fees, and how a lower fee leaves more of the balance earning. What it is, from a markets regulator's bulletin: fees and expenses come with investment products and services, as with anything you buy. These fees may seem small, it says, but over time they can have a major impact on a portfolio. How it works: fees and expenses reduce the amount of money in your portfolio earning a return.

The bulletin's example: $100,000 that grows 4% a year for twenty years. With an annual fee of a quarter percent, it would be worth about $208,000. With a half percent fee, about 198,000. With a 1% annual fee, about $179,000.

In the bulletin's chart, the lowest fee leaves the largest balance after twenty years. The first step, from the bulletin: understanding and comparing the fees you will be charged. For funds, it notes, the prospectus contains a standardized table of fees and expenses. It also says to check your statements, to be sure you are being charged correctly.

What it takes: questions, like which fees you will pay to purchase, hold, and sell an investment. The bulletin is plain: even if you can't readily identify separate fees, you typically pay fees. Investing isn't free. Its limit: the 4% growth is a hypothetical example, not a forecast for any investment.

In some cases, the bulletin adds, fees are negotiable. Fee rules differ from place to place, so check the rules where you live. Quick check for number seven: the fee table read, statements checked, and costs compared before investing. That is all seven; here they are again, each with its first step.

Recap

Number one, compounding: the calculator starts with your initial investment. Number two, interest on interest: savings left in an interest-bearing account. Number three, time: when you start matters, not only how much you save. Number four, frequency: find it in the account disclosures.

Number five, the APY: disclosures show both the yield and the interest rate. Number six, debt: the guide's example lists each card's balance, rate, and monthly interest. Number seven, fees: the bulletin starts with understanding and comparing them. Which of the seven surprised you most?

Tell us in the comments. Results vary, rules differ where you live, and this is information only, not financial advice. Next on Wealth Filings, watch seven ways people make extra money, linked on screen. Subscribe so you see the next list first.