Annualized Rate of Return Formula: Annual Rate = ( ( 1 - ( ( period rate * periods ) / periods ) ) ^ periods ) - 1
Annualized Rate of Return Definition
Introduction This is a very useful financial calculator. Creditors and debtors deal with each other on a wide variety of time frames. Sometimes, creditor-debtor terms are for only a few months, other times for decades. What they all have in common is a requirement to compare dividend rates, also called rates of return. Annualization does that by calculating an equivalent annual dividend rate from a given dividend rate and a non-annual compounding time period. This time period is also expressed in terms of “periods per year,” and refers to how often a given rate is applied and calculated to compounded-interest investments.
Dividend Rate The dividend rate specifies what percentage of an invested amount is paid to the creditor at regular time intervals. In this Annualized Rate of Return Calculator, the dividend rate is entered exactly as a percentage numeric value. For example, 5% would be entered as “5.”
Periods per Year “Periods per Year” refers to the compounding frequency. For annual compounding, periods per year would be one. For quarterly compounding rate there are four periods per year, so the “periods per year” input would be “4.” Similarly, a monthly compounding frequency would give 12 periods per year. A daily compounding rate would give 365.25 periods per year since there are 365.25 days in a year, averaging leap-year effect.
Formula Annualized rate of return is generally calculated as Ra= [(1 + R)^f] – 1.
Ra = annualized rate of return, as a decimal
R = given rate of return in one compounding-frequency timespan.
f = periods per year, also called “compounding frequency.”
Calculation Example Let’s assume we are given a 1.2% dividend, compounded monthly. From this information, we can find the annualized rate of return.
Assign R = 0.012. Note how the percent is converted to a decimal in the calculation. In CalculatorPro, the dividend would be typed in as 1.2.
Assign f = 12. Monthly compounding means twelve compounding periods per year.
Carry out the calculation: Ra = [(1 + 0.012)^12] – 1, Ra = [1.0012^12] – 1 = [1.1538946] – 1 = 0.1538946.
Convert decimal rate of return to percentage: 0.15389 = 15.39% with proper rounding.
Notes and Tips The calculator can accept non-integer dividend rates and compounding periods per year. Omit the percent symbol when entering dividend rate into the calculator. The software assumes a percentage and will not give proper results if non-numeric symbols like percent-signs are entered.
How to Calculate Annualized Rate of Return Let's be honest - sometimes the best annualized rate of return calculator is the one that is easy to use and doesn't require us to even know what the annualized rate of return formula is in the first place! But if you want to know the exact formula for calculating annualized rate of return then please check out the "Formula" box above.