Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Annual Percentage Yield (APY) ====== Annual Percentage Yield (APY) is the true rate of return you earn on an investment over one year, crucially factoring in the effect of [[compounding]]. Think of it as the "what you really get" number. While its cousin, the [[Annual Percentage Rate (APR)]], tells you the simple [[interest]] rate, APY reveals the more powerful reality of your earnings. Imagine you're building a snowball. The APR is the handful of snow you add each time, but the APY represents the total size of the snowball after it has rolled downhill, picking up more snow (interest on your interest) along the way. For any investment where interest is paid out more than once a year, the APY will be higher than the APR. This makes APY an indispensable tool for comparing different savings accounts or fixed-income investments, as it provides an apples-to-apples measure of your potential earnings. ===== The Magic of Compounding ===== The secret ingredient that makes APY so important is compounding. Compounding is simply the process of earning interest on your original investment ([[principal]]) //and// on the accumulated interest from previous periods. It’s a virtuous cycle that can turn modest savings into significant wealth over time. Let's see it in action. Suppose you invest $1,000 in an account with a 10% annual interest rate. * **Without Compounding (Simple Interest):** You earn a flat $100 (10% of $1,000) each year. After two years, you would have your original $1,000 + $100 (Year 1) + $100 (Year 2) = $1,200. This is the world of APR. * **With Compounding (APY):** - Year 1: You earn $100 (10% of $1,000). Your new balance is $1,100. - Year 2: You earn 10% on the //new// balance. So, you earn $110 (10% of $1,100). Your total is now $1,100 + $110 = $1,210. That extra $10 is money your money earned for you. This is the power of compounding that APY accurately reflects. The more frequently interest is compounded (daily, monthly, quarterly), the greater the effect and the higher the APY. ===== APY vs. APR: The Investor's Viewpoint ===== Knowing the difference between APY and APR is critical for managing your finances. They tell two different stories, and you need to know which one to listen to. ==== For Savers and Investors ==== When you are //earning// money—through a high-yield savings account, a Certificate of Deposit (CD), or a [[bond]]—APY is your best friend. It shows you the true growth potential of your money. Banks and financial institutions offering savings products are legally required to show the APY, so you can easily compare offers. * **Rule of Thumb:** When saving or investing, always look for the highest APY. ==== For Borrowers ==== When you are //paying// money—on a mortgage, car loan, or credit card—you'll most often see the APR advertised. The APR represents the basic cost of the loan, but it often excludes certain fees and, most importantly, the effect of compounding interest against you. The true cost of borrowing is better reflected by a concept called the [[Effective Annual Rate (EAR)]], which is calculated just like APY and shows the real damage to your wallet. * **Rule of Thumb:** When borrowing, scrutinize the APR but understand that the true cost, especially on credit cards with compounding interest, is higher. ===== A Value Investor's Take on APY ===== [[Warren Buffett]] famously called compounding "the eighth wonder of the world," and APY is its mathematical signature. For a [[value investor]], understanding this concept goes far beyond choosing a savings account. It’s a fundamental principle for evaluating businesses. A great business is a compounding machine. When a company generates profits, it can either pay them out to shareholders as [[dividends]] or keep them as [[retained earnings]] to reinvest back into the business. A company that can consistently reinvest its earnings at a high rate of return is effectively compounding its shareholders' capital, just like a high-APY savings account. The growth in the company's [[intrinsic value]] will, over time, reflect this compounding power. Therefore, a value investor uses the principle behind APY to ask: "At what rate can this business compound my capital over the next decade?" It’s a shift from just looking at the sticker price of a stock to understanding the long-term economic engine that APY so elegantly describes. ===== The Formula Unpacked (For the Curious) ===== If you want to peek under the hood, the formula for APY is straightforward: * **APY = (1 + r/n)^(n) - 1** Let's break that down: * **r** = The stated nominal annual interest rate (the APR as a decimal). * **n** = The number of compounding periods per year. === Example === Imagine a bank offers an account with a 5% APR (r = 0.05) that compounds monthly (n = 12). - APY = (1 + 0.05/12)^(12) - 1 - APY = (1 + 0.004167)^(12) - 1 - APY = (1.004167)^12 - 1 - APY = 1.05116 - 1 - APY = 0.05116 or **5.116%** As you can see, the 5% APR actually gives you a return of 5.116% over the year, all thanks to the magic of monthly compounding.