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Annual Percentage Yield

Annual Percentage Yield. The Annual Percentage Yield (APY) tells you how much you will earn in a year as a percentage of the investment. This is the standard way of comparing investments. APY is used to compare earnings across different time periods and with different compounding periods.

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Annual Percentage Yield

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  1. Annual Percentage Yield • The Annual Percentage Yield (APY) tells you how much you will earn in a yearas a percentage of the investment. • This is the standard way of comparing investments. • APY is used to compare earnings across different time periods and with different compounding periods. • APY is different than APR (Annual Percentage Rate) because APR does not incorporate compounding within the year. • APR is what we call (r) in most of our interest equations. • For example - $100 is invested for one year at 6% compounded monthly. • b = 100(1+ .06/12)12 = $106.17 • The APR is 6%. The APY is 6.17%. • APY = (1+r/n)n -1

  2. Example less than 1 year • We learned about APY in our compound interest unit. • For example - $100 is invested for one year at 6% compounded monthly. • b = 100(1+ .06/12)12 = $106.17 • Notice that you actually earned $6.17 in one year, which is 6.17% of the amount invested. • The APR is 6%. The APY is 6.17%. • Remember “n” is the number of times per year the interest gets compounded. • In this case n=12 • APY = (1+r/n)n -1

  3. Equations for APV and CAGR • Remember “n” is the number of times per year the interest gets compounded. • APY = (1+r/n)n -1 • APY = (Ending Value/Beginning Value)n -1 • APY and CAGR are essentially the same thing • APY is typically used for short term investments • CAGR is typically used for longer term investments

  4. Another less than 1 year example • When you calculate r/n what you are doing is turning your annual rate into a rate for the time period of compounding. • A rate of 6% compounded monthly… • .06/12 = .005 means that you earn .5% each month. • If you know how much you earned over 6 months, this is a slightly different formula. • Example – you invest $100 and 6 months later your investment is worth $105. This is a 5% return. • APY = (1 + .05)2 -1= 10.25% • APY = (105/100)2 -1= 10.25% • n = # of times compounded per year. • n = 1 year / duration of investment in years.

  5. Example More Than 1 Year • You can also use APY as a benchmark for investments that last more than 1 year. • In this case it is called Compound Annual Growth Rate (CAGR) • Example – You invest $500 in stock. 10 years later the stock is worth $700. Is this a good return? • The total return is (700-500)/500 = 40%. • 40% sounds good, but is it good over 10 years. We would want to know our earnings per year. • The formula below is just like the previous example • CAGR = (1+ r)n -1 • CAGR = (Ending Value / Beginning Value)n -1 • n = 1 year / duration of investment • CAGR = (1 + .4)(1/10) – 1 = 3.42% • CAGR = (700/500).1 – 1 = 3.42%

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