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Money Basics: Simple Interest, Compound Interest, APR and APY

This article was written by in Banking. 4 comments.


April is National Financial Literacy Month in the United States. In most cases, schools do not extensively teach financial skills. Teenagers, highly susceptible to messages from the media, often do not have guidance from teachers, who are not trained to teach financial skills, or from parents, many of whom do not model healthy financial behavior. This series of articles at Consumerism Commentary serves to help inspire discussion about basic financial concepts. Please feel free to forward this article to someone who might benefit from a basic financial overview.

This article covers the staple financial resource for anyone seeking long-term financial stability, the savings account. This is the third article in the Money Basics series; so far this series has covered checking accounts and savings accounts.

What is interest?

Interest is a fee paid for the use of someone else’s money. Any individual or company that lends money will charge the borrower interest, always designated as a percentage like 5%. This percentage is almost always means “per year.” The most common forms of interest appear in savings accounts, where a bank pays you interest for depositing your money in the account, and credit cards and other loans, where you pay a company for allowing you to use their money for a time. Hundreds of years ago, society frowned upon charging interest, but as lending money became more prevalent for uses other than acquiring goods such as modern commerce, the stigma of interest slowly disappeared in many cultures.

The two main forms of interest are “simple interest” and “compound interest.” Simple interest is easily calculated. If you borrow $1,000 from a bank that charges you 5% simple interest, you will owe 5% more than $1,000, or $1,050, at the end of the year if you do not borrow more and do not pay back part or all of the loan. The $1,000 is a “principal.” Multiply the principal and the rate of interest (5% becomes 0.05 when multiplying) to determine the amount of interest ($50). Adding the interest amount and the principal results in the total due after one year: $1,050. With simple interest, if you don’t pay the loan back until the end of the second year, you will have another $50 to pay for a total of $1,100. Your second year of interest is based on your original principal.

Compound interest is more common than simple interest, but there are many nuances. Say the bank charges 5% interest on that $1,000 loan, but it is compounded annually rather than not compounded (simple). At the end of the first year, the first year’s interest, $50, is added (compounded) to the principal. Your second year’s interest is then calculated based on your new principal of $1,050. 5% of $1,050 is $52.50, so rather than owing $1,100 at the end of the second year, you would owe $1,102.50.

If only life were that simple. Interest can also be compounded monthly, daily, or continuously. A 5% interest rate compounded monthly, paid to you by a bank in return for your $1,000 deposit, leaves you with $1,051.16 in your bank account at the end of the year assuming no further deposits or withdrawals. That is a little more than the $1,050 of simple interest or interest compounded annually. If that same 5% interest rate is compounded daily, your ending balance would be $1,051.27. Compounded continuously, the 5% rate would also result in $1,051.27, but a fraction of a cent more than the result of daily compounding.

Banks will usually describe their compounding method in the fine print, but this is only a minor concern for savings accounts, as I’ll explain below.

Don’t be misled by interest rates and terminologies

You would think that all financial terms would carry the same definitions regardless of the circumstances in which they are used. But there is some confusion when comparing interest rates for loans with interest rates for savings accounts. Indeed, there is further confusion when comparing savings account interest rates from one bank to another bank. Here are some tips for discerning the differences.

Loans, like mortgages, are often advertised by interest rate. But sometimes, a secondary rate, is also given. The first rate on the advertisement is the nominal interest rate and the second rate is the effective interest rate; the true cost of borrowing the money including the results of compounding as well as any fees that may be charged. Consider the mortgage loan advertisement I found online yesterday.

Mortgage advertisementThis ad lists an interest rate of 4.625% but the true annual cost is actually 4.879%. This advertiser calls the nominal interest rate the “rate” and the effective interest rate the “APR” (annual percentage rate), and this is common terminology for loans. Lenders are required to clearly display the true annual cost of a loan, the APR, but this often just leads to more confusion.

Unfortunately, savings accounts reverse part of this word usage pattern. A savings account’s APR usually refers to the nominal interest rate, and the true annual result, after compounding based on that particular bank’s method, is called the “APY” (annual percentage yield). For example, in our continuous compounding method mentioned above, while the savings account’s interest rate is 5%, the APY is closer to 5.127%. When banks advertise their savings accounts, they usually include the APY, leaving the nominal interest rate to be found only in fine print if anywhere. The APY is a standard metric that makes it easy to compare savings accounts across banks regardless of the type of interest, and I use APYs to compare high-yield savings rates here.

If you are thoroughly confused, you can always head to dinkytown.net, which offers calculators to help you determine a loan’s APR (true annual cost) if you know the loan’s (nominal) interest rate and fees and to help you compare how much more you would earn by switching to a savings account with a higher interest rate (APY).

Albert Einstein probably never called compound interest “the most powerful force in the universe,” though this quotation or one similar is often attributed to him. If you want to “get rich,” all you need is compound interest, preferably at a rate above inflation, and lots time on your side.

Updated September 17, 2011 and originally published April 22, 2009. If you enjoyed this article, subscribe to the RSS feed or receive daily emails. Follow @ConsumerismComm on Twitter and visit our Facebook page for more updates.

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About the author

Luke Landes, also known as Flexo, is the founder of Consumerism Commentary. He has been blogging and writing for the internet since 1995 and has been building online communities since 1991. Find out more about him and follow Luke Landes on Twitter. View all articles by .

{ 4 comments… read them below or add one }

avatar Bill

You should also make the point that compound interest works in your favor when you are saving. Einstein is reputed to have called it the greatest force in the universe. Don’t ignore when saving or spending.

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avatar Luke Landes ♦127,480 (Platinum)

Bill: I think you skipped the last paragraph. :-)

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avatar sam

This is a great round up of what interest means and gives anyone a clear understanding. A real help for those people that have been misled in the past which from the data that is constantly coming out at the minute about banks misleading people.

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avatar Tim

Woohoo! Go Financial Literacy Month! Nice work getting doing your part to educate, Flexo!

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