# Investment Return Calculations

Investment returns should be evaluated and compared in reference to a specified length of time. A 7% total return is not meaningful performance data without knowing the length of time it took to earn the 7%. Likewise, comparing a 7% total return over three years versus a 7% total return over five years will not provide a fair comparison. To help people better evaluate and compare total investment returns over various time periods, they are often calculated as annual returns. Let’s examine how total returns and annual returns are calculated.

Assume a \$10,000 investment grows to \$12,000 over a five year period. To calculate the total return over the period, divide the ending value by the beginning value and then subtract one. [ (12,000/10,000) – 1 = 0.20 = 20% ] It might seem like a 20% return over five years would equate to a 4% annual return. [ 20% / 5 = 4% ] However, calculating annual return this way ignores the benefit of compound interest. Compound interest occurs when investment earnings are added to the principal investment so that future investment growth applies to both the initial investment and accumulated earnings. If we assume the investment earns 4% per year on both the initial investment and the accumulated earnings, the total return after five years would be more than 20%. Therefore, simply dividing the total return by the number of years of the investment period is not the correct way to calculate annual return.

To calculate annual return on both the initial investment and the accumulated earnings over the period, divide the ending value by the beginning value to derive the total return, raise the total return to the power of one divided by the number of years of the investment period, and then subtract one. [ Annual Return = (ending value / beginning value)^(1 / number of years) – 1 ] When we know the annual return but not the total return, we can calculate total return by adding one to the annual return rate and raising it to the power of the number of years of the investment period. [ Total Return = (1 + annual return)^(number of years) ]

Let’s return to the example where a \$10,000 investment grows to \$12,000 over a five year period. The annual return is calculated as [ (12,000/10,000)^(1/5) – 1 = 0.0371 = 3.71% ]. Using the annual return number of 3.71%, we can calculate the total return over five years as [ (1+0.0371)^(5) – 1 = 0.1998 = 19.98% ] which when rounded, is the 20% total return we initially calculated. The same formulas apply even if the investment period is less than one year. Assume the \$10,000 investment grows to \$12,000 over a nine month period. Nine months is 75% of one year, so the annual return is calculated as [ (12,000/10,000)^(1/0.75) – 1 = 0.2752 = 27.52% ].

In the formulas, when we raise a number to the power of a number, that means we multiply a number times itself for the number of times of the power. [ example: four raised to the power of three = 4^3 = 4*4*4 = 64 ] This part of the formula can get complicated, so a calculator is highly recommended for performing investment return calculations. Investment return itself is not difficult to derive with the use of a calculator. Knowing and using the correct formulas is the key to successfully calculating investment returns. Recognizing the difference between total return and annual return is essential to evaluating and comparing various investment returns.