Understanding Compound Interest – A Complete Guide


As you’re comparing financial investment vehicles, it’s critical that you understand how each vehicle works so that you can maximize your earning potential. There’s nothing like depositing money that you’ve already earned into the right account so that the balance can grow on its own. Essentially, if you open the right type of account, your money can earn money with no effort on your end. This is an effective way to expand your investment portfolio and eventually build a sizable nest egg.

Soon-to-be investors put so much focus is put on choosing the right investment account that they fail to do their research on the one component of investment that makes money grow at an exponential rate–interest. You can deposit money into a savings account, annuity, investment fund, government-issued bond, college savings account, or money market account, but if you don’t understand how interest works, you could be minimizing your return on investment without even knowing it.

The key to making the best investment decisions is to choose a vehicle that earns interest at a faster rate than other products that you have access to. At surface level, the concept of interest seems pretty straightforward. A lot more goes into calculating Annual Percentage Rates and Annual Percentage Yield than you might initially think. To earn the most money on your initial deposit, you should choose an account that earns compound interest. Here’s a complete guide to compound interest so that you can see why this method of growth benefits you.


What is interest?

Before you start to delve into the process of compounding interest, you need a full understanding of what interest is. Just like in college, you take introductory courses before you dive into the focused curriculum. If you’re not introduced to interest and the types of interest that accounts can earn or borrowers can be charged, you’ll already be at a disadvantage.

At the most basic level, interest is the cost of using someone else’s money. An interest rate is generally determined when a contract is created. If you are the borrower on that financial contract, you’ll be the person paying the agreed interest rate. If you’re the lender, you’ll be party on the contract who is paid the interest.


Why is interest paid to an investment account holder?

If you’re doing all of this research to learn about interest and how you’ll earn money on your investment, it might be odd to hear this type of transaction referred to as “lending money” to another party. Believe it or not, when you open a savings or investment account and deposit money into it, you are essentially lending your extra money to the bank so that the bank can then lend that money out and earn their own interest on it.

So whenever you’re opening these savings accounts as investment vehicles to add to your portfolio, you can say that you’re the lender and the bank is a sort of borrower. Since the bank then has the right to use money sitting in your account, you’ll be earning interest on your money. If you didn’t receive any benefits for leaving your money in an investment account, it would completely change the way the finance industry worked today.


Why do you pay interest when you borrow money?

Interest works both ways. You can earn interest as the account holder but you can also be charged interest if you’re classified as the borrower. This is how the finance industry goes full circle. After all banks and credit unions would never profit if they just paid their account holders interest without finding a way to profit. This is where their lending activities come into play.

If you’ve ever taken out an auto loan, secured a mortgage, been approved for a personal loan, accrued student loan debt, or used credit cards, you’ve been on the borrower end of the spectrum. When you’re the borrower, you’ll have to look over quoted interest rates closely so that you calculate how much a loan or credit will cost you in the end.


Why do you earn less than banks when you lend money?

Unfortunately, you don’t fare as well as the lender does when you’re a borrower. When you’re lending out your own money, you’re not going to find a lender that will pay you a double-digit interest rate. It’s not uncommon, however, for a bank to charge you high interest rates to borrow money. This is how the bank profits when they’re borrowing money from investors and using that money to lend out to others.

Some loans carry lower interest rates than others, specifically loans that are secured by collateral. Examples of these loans include auto loans and mortgages. Unsecured forms of credit will carry higher interest expenses. At the end of the day, the bank has to factor in the risk of default, how much money will be lent out, how long the amortization period is, and what the profit will be at the end the period when calculating an interest rate.


How are interest rates calculated?

Interest rates can change on a daily basis. One day you could be charged a very low interest rate to borrow money and if you don’t act quickly, the rate could change in the blink of an eye. To understand why interest can change from one day to the next, you have to learn what lenders use to determine how much they should charge their borrowers.

There are several different forces that influence interest rates. The most basic way to look at fluctuating interest rates is to look at inflation. Generally speaking, the higher the inflation rate, the more interest lenders are likely to charge. This is primarily because in a free market economy high inflation decreases a lender’s purchasing power because the value of their money is lower. Here are some other forces behind fluctuating interest rates:

  • Federal Reserve requirements
  • Supply and demand for loans
  • Economic conditions
  • Consumer confidence
  • Wage inflation
  • Unemployment rates
  • Exchange rates
  • Risk of default


What Does Compound Interest Mean?

There are two different types of interest: simple and compound. These two terms are what make interest rates so very complex. The term simple interest refers to a fixed or non-growing form of return. The term compound interest refers to a growing form of return. When interest is compounded, the lender is earning money on growth that has already been reported in previous periods.


Different Interest Calculation Formulas

If you’re a math whiz, it might be easier for you to grasp the concept of simple interest and compound interest by looking at the formulas that are used to calculate each. When you’re looking at the formulas that are used for calculating lending and borrowing rates, they will all take into account the same details. Here’s what each term in the following formulas mean:

  • P = principal of the loan or your initial investment
  • r = interest rate per year
  • n = number of periods under the loan or account term

Now that you know what each exponent means in the formulas that are used in finance concerning interest rates, you can dive deeper into understanding how simple interest and compound interest is ultimately calculated by actuaries. Here’s a breakdown of the formulas that are programmed into the most advanced interest calculators:

  • Simple Interest (fixed/no growth) : P x (1 + r x n)
  • Compound Interest (changes annually) : P x (1 + r)^ n
  • Compound Interest (n times per year) : P x (1 + r/n)^ nt


Understanding APR vs. APY

Now that you have an basic understanding interest and how it works both ways, it’s important that you can differentiate certain interest-related terms like APR and APY. While some people use these terms interchangeably, they are far from the same thing. If you don’t understand the difference between the two terms, it will work in the bank’s favor.

A high APY can be beneficial when you’re lending money, but it’s the last thing that a borrower would advertise to potential clients. As misleading as it might sound, banks are only going to highlight one piece of the puzzle and not the other. If you want to make informed decisions, here’s a breakdown of what each term means and what you should be looking for depending on the type of account you’re opening:


APR means Annual Percentage Rate

If you’ve ever shopped the market for an affordable auto loan and you have good or Tier 1 credit, you’ve probably received mailers that stressed that the bank offers the lowest APR on the market. APR stands for Annual Percentage Rate. It is the percentage of interest that’s charged within that year. What banks don’t tell you is it’s the annual periodic rate without taking into account interest compounding.


APY means Annual Percentage Yield

If you’re the lender rather than the borrower, you’ll see different focuses on advertisements that interest you. When you’re looking for the best deposit account, the financial expert you speak with will always put most of the focus on quoting the on the Annual Percentage Yield instead of the Annual Percentage Rate. Before you can understand why, you need to understand what APY really means.

Annual Percentage Yield refers to the method of interest calculations that takes compounding into account. It is a higher rate than the APR because it takes into account how much interest is being charged on interest. If the APR is 12 percent (a periodic rate of 1% per month), the APY would wind up being 12.68% because interest is compounded monthly. Therefore, the interest charged, or earned, over the period would be higher than it would appear.


Compound Interest Could Be Good or Bad

Banks are smart. That’s why they quote one interest rate as opposed to the other depending on the type of account or loan being offered. Compounding interest can be a great thing or it can be a terrible thing, it all depends on what side of the table you’re sitting on.


Compound Interest for the Borrower’s Perspective

In a scenario where you’re the borrower, you would prefer to avoid loans where the interest charged is being compounded. To fully understand why, you have to consider a relevant scenario. A borrower applies for a loan to buy a $15,000 vehicle. After taxes and titling fees are calculated, a total of $17,400 is borrowed. This is called the principal on the loan.

If you were this borrower in the above scenario, you will obviously search for the loan from the lender that charges the lowest rate. Unfortunately, if you don’t look at both the APR and the APY, you could choose a loan that’s disguised to have a lower rate when in reality it doesn’t. This happens when the bank offers a compound-interest auto loan that carries a much higher APY interest rate.

This borrower who entered into an auto loan contract was enticed by the 5 percent APR interest rate quoted but they didn’t realize that, after intra-year compounding, the interest charged in the loan throughout the entire year was upwards of 6 percent. This is because interest will be charged on interest every period. As a borrower, it’s in your interest to ask for APY quotes if you ever take out a compound-interest loan.


Compound Interest from a Lender’s Perspective

If you’re the lender who is opening a deposit or investment account, the bank or credit union is going to shift the focus on the quote to showing how high their APY is. By stressing that the bank offers a higher APY than others, the bank looks like it is being more generous to investors than other competitors.

Focusing on APY instead of APR is a common advertising tactic for deposit accounts because that number shows how much you’re going to earn after factoring in the compounding interest. From the lender’s perspective, the compounding is a good thing. You’re essentially earning money off of the money that you’ve already earned. By quoting you the APY on the money that you’ve invested, you’ll believe you’re getting a higher rate of interest.


Understanding Growth on a Deeper Level

There are so many different definitions used and algorithms that it might seems as if financial experts are making the concepts of simple interest and compound interest more difficult than it needs to be. If you’re really interesting in seeing which option is going to benefit you the most as a depositor, it’s best that you take a deeper look into growth.


Simple Interest Growth is Simple

Understanding growth of investment accounts is easy if you’re choosing a simple interest account. If the interest that your account is earning is calculated based on the simple interest formula, the money in the account will sit there and grow by a specific amount each period. The amount that the principal grows by over the period won’t change because the principal is the same each period.

This type of growth is very straightforward because no compounding is done. Your interest earnings will create something that isn’t reinvested and will not grow more. If you’re looking for a simple and predictable way to invest money without having to worry about reinvestment calculations, this is an easy concept to master. Take the following investment scenario into account:

  • Starting Principal : $500
  • Years : 10
  • Annual Percentage Rate : 10%

You won’t earn interest on your interest with a simple interest investment vehicle, but you will still earn a fixed amount. Here’s a breakdown of how a deposit account would grow by using simple interest growth formulas over the entire term (10 years):

  • Year 1 : interest earned $50
  • Year 2 : interest earned $50
  • Year 3 : interest earned $50
  • Year 4 : interest earned $50
  • Year 5 : interest earned $50
  • Year 6 : interest earned $50
  • Year 7 : interest earned $50
  • Year 8 : interest earned $50
  • Year 9 : interest earned $50
  • Year 10 : interest earned $50

End of Year 10:

  • Total Interest Earned – $500
  • Total Account Balance – $1000


Compound Interest Calculations When Interested in Compounded Annually

Compounded interest formulas definitely make calculations more difficult. If you’re not a number cruncher, you might be better off seeing how your investment account will earn money over the same 10-year period as the simple interest account above.

As previously mentioned, compound interest grows at a faster rate. That’s because you’re earning interest on the interest that you had already earned the period prior. How often and how fast the interest grows will depend on the period. To compare simple interest and compound interest growth rates, it’s easiest to look at the scenario that was already used. Here’s a reminder:

  • Starting Principal : $500
  • Years : 10
  • Annual Percentage Rate : 10%

The easiest way to calculate compound interest is when it’s calculated annually as opposed to semi-annually, quarterly, or monthly. It might not show you the fastest rate of growth but it’s a good starting point. Here’s a look at the growth if the scenario above compound interest grows annually:

  • Year 1 : interest earned $50
  • Year 2 : interest earned $55
  • Year 3 : interest earned $60.50
  • Year 4 : interest earned $66.55
  • Year 5 : interest earned $73.21
  • Year 6 : interest earned $80.52
  • Year 7 : interest earned $89.10
  • Year 8 : interest earned $97.43
  • Year 9 : interest earned $107.18
  • Year 10 : interest earned $117.90

End of Year 10

  • Total Interest Earned – $1296
  • Total Account Balance – $1796


How Does the Compounded Period Affect the Growth?

As you can see, choosing an investment account that compounds interest is the best option if you’re interested in growth, as pretty much all investors are. Not only can the way that interest is calculated affect your portfolios potential to grow, the compounding period will also have an impact.

There are a few different compounding periods. The easiest way to do the calculations is to compound the interest at an annual rate but some accounts will have interest rates that will be compounded more often. You should always ask the bank hour often interest is compounded before choosing just any type of investment product. For some accounts, there’s an industry standard period and for others it’s up to the bank.

The more often the rate is compounded, the better it is for the deposit account holder. It essentially means that the interest will grow more often. For compounding that’s done quarterly instead of annually, it offers you growth 4 times per year instead of once. Here’s how much your investment would have grown by if it was compounded more than just annually:

  • Compounded Semi-Annually
    • Total Interest Earned: $1326.65
    • Total Account Balance: $1826.65
  • Compounded Monthly
    • Total Interest Earned: $1353.52
    • Total Account Balance: $1853.52
  • Compounded Daily
    • Total Interest Earned: $1358.95
    • Total Account Balance: $1858.95


The Key Things to Know About Compound Interest

As you can see, when it comes to investing compound interest is a good thing. It’s not such a great thing when you’re paying extra interest on money lent to you as a borrower. If anything, you should take at least the following key points away from this guide:

  • If you invest in a compound interest account you can watch your money grow faster than other accounts as long as you leave the earnings in the vehicle
  • The longer that you have to let the interest compound, the more it will grow
  • Money will add up in your investment accounts faster than you think
  • If you’re paying minimums on a debt where interest is compounded, you could be paying down your balances for a long time
  • You can use interest earned to pay down other debts so you avoid making unnecessary interest payments


What Types of Investment Accounts Earn Compound Interest

Not all types of investment accounts earn compounded interest. It’s best that you differentiate the account types so that you’re investing your money in the best places that will offer you a higher rate of growth. Here are some of the accounts that earn compound interest:

  • Savings accounts (compounded annually)
  • Money market accounts
  • Certificates of Deposit
  • Zero coupon bonds
  • Annuities
  • Some permanent life insurance policies


How Are Compound Interest Earnings Taxes?

One of the drawbacks that some don’t consider until it’s too late is what their tax liabilities will be if investing in a compound interest account. You’ll earn more interest throughout the year that someone who chose to invest in a fixed interest earning account, but that doesn’t mean that some of those earning won’t be eat up when it increases your tax burden.

The IRS can collect taxes on any investment interest that you’ve earned during the tax year if the investment wasn’t made into a tax-sheltered account. The tax rate will be determined by your regular income tax rate. If you’re currently in the taxable income rate of 30% and your earnings are taxed, that means that your rate of return will be reduced dramatically. A 10 percent return could go down to a 6 percent return after all is said and done.


What is the solution to avoid taxes now?

Instead of investing in a vehicle where growth is taxed each year, it’s best for younger investors to select a tax-sheltered account. One option would be to invest your money in to a tax-deferred retirement account so that you don’t pay taxes on the growth until you retire. The strategy here is that you’ll be in a lower taxable income rate by the time you want to withdraw the money.

Another solution would be to purchase municipal bonds with reinvested dividends that are free of federal tax. By doing this, the dividends that are paid will be used to purchase more bonds so that the money isn’t taxable for the tax period. You could also invest in tax-deferred annuities that pay a lump sum or a monthly benefit when you reach a certain age.


Benefit from the Power of Compounding

As an investor, you will take the power into your hands if you use compounding to your advantage. Earn money off of the growth of your money and watch your nest egg grow. While there can be tax consequences, there is always a way for you to reduce your liabilities if you plan properly.