What Is Compound Interest?

What Is Compound Interest?
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Whether you're taking out a loan or depositing some funds in a savings or retirement account, you're likely to either pay or receive interest in return for money borrowed or saved. In many cases, you'll end up dealing with compound interest, which means you not only accrue interest on the original sum but on top of the interest that accumulates over time as well. While this is good news if you're getting paid interest on deposited funds, it means additional costs if you're a borrower. So, it's crucial to learn how compound interest works, how you can calculate it in different scenarios and how it differs from simple interest.

Understanding the Basics of Interest

When you encounter interest on a loan, credit card or savings account, you can consider it a fee charged or paid in exchange for borrowing, either from your end or the bank's end. In the case of a loan or credit card, you're paying the interest since the lender or creditor is letting you use their money. But in the case of a savings product, the bank will be paying you for the benefit of allowing them the privilege to hold your money and invest or lend it to others.

Depending on the financial product, you'll face either simple or compound interest, and these work differently and have their own formulas and pros and cons. In the case of simple interest, interest just builds on the principal amount, which is the amount you received as a loan or the amount you deposited. However, it's more common to find yourself dealing with compound interest, which means that you either get or pay interest based on the amount of interest accrued already plus the principal.

Regardless of the type of interest, the actual rate can depend on various factors that range from the financial institution and type of financial product to your creditworthiness and current market conditions. For example, your mortgage interest rate can depend on your credit score, location, home cost and loan type, while your savings account interest rate can depend on the bank, amount deposited and tier of account you have. The Federal Reserve has a role in changing interest rates in response to changing economic conditions like unemployment levels, economic growth and inflation.

Read More​: 7 Kinds of Interest Rates

Exploring Compound Interest

When you get a student loan, personal loan, credit card or savings account, there's a good chance that the financial institution will use compound interest rather than simple interest when calculating what to charge or pay you. Depending on the financial institution and type of account, you'll find that the interest will compound as often as daily or as little as annually. It's also common for interest to compound on a monthly or quarterly basis.

This compounding period is important since it impacts the annual percentage yield. This differs from the annual percentage rate, or APR, that you often see advertised as the interest rate, as the APY provides the most realistic interest rate that applies to your financial product. The more often the interest accrues, the more it will build up, so daily compounding interest adds up slightly more than monthly compounding interest, for example. You can use the formula APY = (1 + r/n)^n - 1 to convert from APR to APY, where r is the APR and n is number of times each year that the interest compounds.

Knowing how compound interest works is especially important for investors who seek the biggest return on their money. The Rule of 72 is often used as it provides a quick glance at how long someone needs to invest their money to build up enough compound interest at a set rate to double their investment. It's often used for lower interest rates where there's higher accuracy, and it involves simply dividing the number 72 by the annual interest rate to get a number of years. For example, if you only earn 2 percent interest on an investment, then you'd divide 72 by 2 to see it would take around 36 years to double your money.

Learning the Compound Interest Formula

To calculate how much compound interest accrues on your loan or investment, you can expect to use a more complex formula than you would with simple interest. That's because the formula has to account for the frequency of compounding. However, you won't need to do work beforehand to determine the APY from the APR since the formula will handle this in the calculation.

The compound interest formula is A = P(1 + r/n)^ (n * t). To break down the formula, the r refers to the APR as a decimal, the n refers to the compounding frequency, the t refers to the number of years for the loan or investment and the P means the principal. The A is the resulting total principal and accumulated compound interest over the term. When using this formula, keep in mind that rounding numbers can give you considerably different results in some cases, so it helps to round further out for more accuracy.

Since it can be easy to make mistakes with the math, using a compound interest calculator like the one available on the Investor.gov website can save you time and help you run different scenarios for borrowing and investing decisions. You'll just need to know the initial principal, term length, APR and compounding frequency to use this tool. An advantage is the online calculator can easily account for additional deposits you might make to your savings or investment account.

Comparing With Simple Interest

Before getting into some sample calculations, it helps to compare compound interest with simple interest. This type of interest is what you'll more often see with auto loans, personal loans, mortgages and some types of savings accounts. Since interest doesn't build on interest, this feature offers an advantage for people borrowing money but disadvantages those who are saving or investing.

The fact that interest only builds on the principal means that you'll find simple interest much easier to calculate than compound interest. To do the calculation, you can use the formula I = P * r * t, where you multiply the principal times the APR in decimal form times the number of years in the term. This gets you the interest accrued, which you can easily add to the principal to get the total amount of principal plus interest.

While you can easily calculate simple interest by hand or with a regular calculator, you can find tools online like the simple interest calculator from MoneyChimp that lets you run scenarios quickly and compare the result with what compound interest would have looked like.

Compound Interest Calculation Example

You can best see the impact of compound interest with an example that shows how it benefits savers and disadvantages borrowers. Consider you're dealing with $5,000 for the principal, 4 percent for the interest rate and a five-year term.

As you've learned, the compound interest formula to find the amount with interest is A = P(1 + r/n)^(n*t), where P is the principal of $5,000, r is the 4 percent interest rate converted to the 0.04 decimal form, n is 365 for daily compounding, and t is 5 for the term in years. Plugging all these figures in, you'd get ​A = $5,000(1 + 0.04/365)^(365*5)​ initially. After dealing with the calculations within the parentheses and using some rounding, you'd get A = ​$5,000(1.00011)^(1,825)​. This works out to ​A = $5,000 * (1.22231)​, which finally simplifies to ​$6,111.55​ in interest and principal paid.

As a borrower, this would mean that you end up paying $1,111.55 in combined interest on your loan over those five years. The entire amount paid back including the principal would be $6,111.55. On the other hand, if the $5,000 was saved under the same terms and you made no additional contributions, you would have earned the $1,111.55 in interest over the five years and ended up with a $6,111.55 balance in your savings account.

Simple Interest Calculation Example

To see the lower interest paid and earned when you're dealing with simple interest, consider that you're dealing with the same $5,000 in principal, interest rate of 4 percent and a term of five years, except this time it's simple interest. You can use the simple formula I = P * r * n to get the amount of interest paid, where P is $5,000, r is 0.04, and n is 5. Plugging in those numbers, you get ​I = $5,000 x 0.04 x 5​, which works out to ​I = $1,000​ in interest. This means a total principal and interest amount of ​$6,000​.

If you had taken out a loan with these terms, this means that you would end up paying $1,000 in interest over the term, and this is $111.55 less than with daily compounding. This works out to $200 paid per year. When adding this $1,000 in interest to the principal for the loan, it means you would pay back $6,000 altogether versus the $6,111.55 with compounding daily interest.

On the other hand, consider that you had instead deposited that $5,000 into a savings account with the same terms. After you had kept all the money in the account for five years, you would have accrued $1,000 in earnings, or $200 per year. This means you'd have the $6,000 in hand, which is $111.55 less than you'd have with daily compounding interest.

Compound Interest Tips for Borrowers

As you've learned, compound interest is more of an enemy when you're a borrower due to the added costs. This means you should take steps to get the best interest rate beforehand and then make good debt payment decisions that minimize the interest charged over the term.

When borrowing, shop around for low interest rates on loans or credit cards and compare a few options while also considering any fees that will add to the interest costs. Since your interest rate can depend on your credit history, it can also help to work on paying off existing debt or fixing errors on your credit report so that you don't face both difficulties borrowing and unfavorable interest rates.

Once you start making payments, make them on time to avoid fees and interest rate increases, try to pay more principal each month when you can and aim to pay credit cards in full since they tend to have the highest rates. If you have extra cash, try to use it to pay off your debts that charge the most interest and then work your way down to debts with lower rates. You can consider debt consolidation or refinancing if your credit situation changes where you can possibly get lower rates, but keep in mind that the fees involved might wipe out most of the potential interest savings in some cases.

Compound Interest Tips for Savers

Whether you're working on long-term savings for retirement or short-term savings for a personal goal, compound interest can work in your favor. For the best results, you'll want to contribute as much as possible to your savings and find the right investment and savings products that offer competitive interest rates and accrue interest frequently.

As a saver, you'll also want to shop around for the highest interest rates and aim for savings products like certificates of deposit and money market accounts versus traditional savings accounts that can yield very low rates. When you have extra money and want a higher possible return, you can look into retirement accounts and investments. However, keep in mind the market fluctuations that can also result in losses with these riskier investments, at least in the short term.

By putting as much money as possible into savings and adding more regularly, you can get more interest. Some banks may have bonuses for accounts with high balances that can lead to even more of a return.