Many investments will increase in value and earn a compounded return as time progresses. Investors can use the natural log function to calculate the continuously compounded rate of return on stocks and bonds. The continuous compounding rate of return assumes that you're constantly reinvesting your earnings at the same rate of return.

## Log Return for Bonds

To calculate the natural log return for bonds, you must first identify the stated interest rate. Most bonds clearly state the interest rate as part of of the bond title. In a spreadsheet, enter the formula, "=LN(1 + stated rate of interest)" into a cell. For example, a bond with a 9 percent interest rate would read "=LN(1.1). The resulting figure is the continuously compounded annual rate of return on the bond.

## Log Return for Stocks

Unlike bonds, stocks don't pay owners a predetermined interest rate. However, the price of many stocks increases over time. To calculate log return, you must first find the initial value of the stock and the current value of the stock. In a spreadsheet, enter the formula "=LN(current price/original price)." For example, if you purchased a stock for $25 a share that is currently $50 a share, you would enter, "=LN(50/25)." The resulting figure is the continuously compounded rate of return for the stock for that time period.