# Formula & How to Calculate

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130 Compound interest is a powerful tool for building wealth. It’s also a devastating tool that can destroy wealth. It just depends on which side of the financial equation you use it.

On the positive side, compound interest makes the return on investments (e.g. savings, retirement accounts) grow quicker and more substantially over time.

On the negative side, it makes debt (e.g. credit cards) grow quicker and more substantially over time.

The math for compound interest is simple: Principal x interest = new balance.

For example, a \$10,000 investment that returns 8% every year, is worth \$10,800  (\$10,000 principal x .08 interest = \$10,800) after the first year. It grows to \$11,664 (\$10,800 principal x .08 interest = \$11,664) at the end of the second year.

In 25 years, that initial investment of \$10,000 would grow to \$68,484, thanks to compound interest.

Unfortunately, the same math applies to credit card debt, only in a very negative way.

The average credit card interest rate in the summer of 2018 was 17% APR. If you owe \$5,000 in credit card debt and make only the 4% minimum payment due, you would have \$71 of interest added to your balance so you would now owe the card company \$4,871.

If you didn’t use that card at all, and continued to pay the 4% minimum every month, it would take 10 years and 10 months) to pay off the debt. You would pay a total of \$7,627 – including \$2,627 of interest – to pay off what started out as a \$5,000 debt.

That is the negative power of compound interest!

## What Is Compound Interest?

You might have learned about compound interest as a kid when you opened a savings account and the bank added it to your balance every month. As pleasing as it is to earn money for doing nothing more than keeping it in an account, you probably have learned that compound interest is a double-edged sword.

Banks are in business to borrow your money at a low rate and lend it at a higher one. Deposits are one way banks borrow. They pay you for the right to use your deposits to make loans. They use compound interest on both ends of the equation, paying depositors and charging borrowers, and make money on the spread – the difference between the interest they pay depositors and the interest they charge borrowers is bank revenue.

Most of us are on both sides of the equation. We earn interest on checking and savings accounts, and we pay interest on mortgages, car loans and credit card balances.

The key is the what financiers call the “time value of money.” The longer your money is in the bank, the more it grows. As interest is added to the balance, you have a larger balance and earn more interest. But if you’re borrowing money, say with a credit card, the reverse is true.

On both sides of the equation, compound interest, which is really interest paid on interest, makes deposits and debts grow more quickly.

## How Compound Interest Works

There are two ways to calculate interest – simple and compound – and they are very different.

Simple interest is a set percentage paid on the initial principal. If you borrowed \$1,000 and agreed to pay it back three years later at 20% annual interest, you would owe \$600 interest plus the \$1,000 principal you borrowed.

If you had a \$1,000 loan with interest that compounded 20% annually, you would owe 20% on the annual balance, which would increase every year. After three years, you would owe \$1,728 — \$1,000 in principal and \$728 in interest because every year the previous year’s interest is added to the principal.

Most loans don’t compound annually, but instead use a daily, weekly or monthly increment. More frequent compounding means your money will grow more quickly if it is in a bank account. If it is a debt, the amount you owe also will increase more rapidly.

It’s important to know that few compound loans or deposit accounts use an annual formula. Some loans and deposits can compound monthly, weekly or daily. The shorter the interval, the greater the frequency that the loan interest accrues. Payday loan businesses often use short compounding periods

When evaluating a deposit or a loan, you should look at total interest paid, the frequency the loan compounds and the annual percentage yield, known as the APY. Those three factors can be used to determine your annual interest rate.

The compounding frequency is the number of times a year the balance compounds. If your loan compounds weekly and carries 5% interest, you pay 1/52nd of 5% each week. You don’t pay 5% a week on the balance. Since the balance changes as the deposit or debt compounds, the amount you owe 5% on increases with each compounding period, so you wind up paying somewhat more than if the loan only compounded once a year. The same rule applies to a savings account in which you receive compounding interest.

The annual yield is complicated by the number of days you have money deposited or borrowed. If the money is untouched for a year, this simple formula will give you the annual yield: APY = 100(Interest/Principal). If a bank pays \$61.68 in interest for 365 days on a \$1,000 deposit, the formula would be:

APY = 100(61.68/1,000)

APY = 6.17%

Using a variation of this formula is also useful if the interest rate changes during the year. If a bank offers a 5% interest rate compounded daily on a six-month certificate of deposit for three months, and then a 5.5% interest on the next three months and the total interest is \$26.68, using a modified formula that factors in the number of days will reveal an APY of 5.39%.

## How to Take Advantage of Compound Interest

Compound interest can help you build savings over time, though in recent years low interest yields make a conventional bank savings account a poor investment if your goal is income or growth. Mutual and money market funds, certificates of deposit and exchange traded funds have proven much more reliable vehicles for building wealth.

That said, money invested in a compounding account will grow over time, and if you make regular deposits, it will grow faster. The key is longevity of the investment. If you move money in and out of a savings account, you will diminish its potential. No matter how much money you put into a savings account it will grow at the same rate. You should understand how much interest you will be paid and how often it will compound.

Interest rates change over time, and you should keep track of them. Even though an account using compound interest will grow faster than one the relies on a simple interest calculation, if the interest rate is very low, as it typically has been during the past decade, it will be a slow process. The advantage is the deposits in federally insured institutions are insured by the Federal Deposit Insurance Corp., so you can’t lose money like you can with other investments.

No matter how much money you deposit into a savings account, the rate of return is the same even though the return in dollars grows substantially if you deposit more money.

Finally, remember the flip side. If you have a debt that uses compound interest, the amount you owe will grow each time the interest compounds and your payments will get larger over time. For that reason, it is wise to pay down compounding debts as quickly as you can.

## The Rule of 72

You could use a calculator to project how much interest you will earn over time. Some calculators are programmed to compute interest, others require you to write a formula and plug in the numbers. Another method, called the rule of 72, gives you an easy way to learn how long it will take to double your money.

The rule of 72 factors in the interest rate and the length of time you have your money invested. To use the rule, you multiply the number of years you plan to have your money invested by the interest rate. When the product is 72, your money is doubled. The formula allows you to solve for the length of time it will take you to double your money at a certain interest rate and for the interest at necessary to double over a length of time.

#### Here are two examples:

• You have \$2,000 saved at 4% APY (annual percentage yield). How long will it take to double your investment? To get the answer, divide 72 by 4, so it would take 18 years to double your money.
• If you have \$500 and wanted to double your money in 10 years, how much interest would have to earn? The answer that, divide 72 by 10. The result, 7.2, tells you need a 7.2% APY to double your money in 10 years. That would be difficult to accomplish at today’s interest rates, so you might need to invest your money in a higher-yielding investment.