This Annualized Return Calculator helps you determine the rate of return you earned on an investment over a multi-year period, smoothed out on a yearly basis. It is crucial for comparing investments with different holding periods.
Annualized Return Calculator
Please ensure only one field is left blank to solve for it, and all inputs are positive numbers.
Calculated Result:
Detailed Calculation Steps
Annualized Return Formula
Formula Sources (Academic/Finance): Investopedia – Annualized Return, TreasuryDirect – Rate of Return
Variables
- PV (Present Value): The initial amount of money invested or the starting capital. Must be positive.
- FV (Future Value): The total value of the investment at the end of the period, including principal and accumulated gains/losses. Must be positive.
- T (Time): The length of the investment period, expressed in years. Must be positive.
- ARR (Annualized Rate of Return): The geometrically averaged amount of money earned on an investment each year over a given time period, expressed as a percentage.
Related Calculators
- Compound Interest Calculator
- Time Value of Money (TVM) Calculator
- Internal Rate of Return (IRR) Tool
- Capital Gains Estimator
What is Annualized Return?
Annualized Return represents the average growth rate of an investment per year over a specified period. Unlike the cumulative return (which measures total change over the entire period), the annualized return provides a standardized, easily comparable metric. This makes it the go-to measurement for evaluating the performance of different assets or fund managers.
It is calculated using the geometric mean, which accounts for the effects of compounding. The concept is based on the premise that the growth rate is constant each year, smoothing out the volatility and performance fluctuations that occurred during the actual holding period. Therefore, an 8% annualized return means the investment performed as if it grew by exactly 8% every year, compounded annually.
How to Calculate Annualized Return (Example)
Let’s find the ARR for an investment:
- Determine the Initial Investment (PV): Suppose you invested $10,000.
- Determine the Final Value (FV): After 7 years, the investment is worth $18,000.
- Determine the Time Period (T): The investment was held for 7 years.
- Calculate the Return Ratio: Divide FV by PV: $18,000 / $10,000 = 1.8$.
- Apply the Time Exponent: Since T = 7, the exponent is $1/7 \approx 0.142857$. $1.8^{0.142857} \approx 1.0876$.
- Subtract 1: $1.0876 – 1 = 0.0876$.
- Convert to Percentage: $0.0876 \times 100 = 8.76\%$. The Annualized Rate of Return is 8.76%.
Frequently Asked Questions (FAQ)
What is the difference between Simple Return and Annualized Return?
Simple (or Cumulative) Return is the total gain or loss over the entire period. Annualized Return is the average, compounded return per year, which allows for fair comparison regardless of the holding period.
Can the Annualized Return be negative?
Yes. If the Future Value (FV) is less than the Present Value (PV), the ratio (FV/PV) will be less than 1, and the resulting Annualized Return (ARR) will be a negative percentage, indicating a loss.
What is a “good” Annualized Return?
A “good” return is relative. Historically, the S&P 500 has averaged around 10% before inflation. For long-term investments, anything consistently above market averages is generally considered excellent.
Why is the ARR calculation important for investment comparison?
ARR standardizes the investment period. Without it, you might incorrectly compare a 50% return over 10 years (low ARR) to a 10% return over 1 year (high ARR). ARR brings both returns to a comparable yearly baseline.