Returns

Simple return:

Future value, using a simple return

Multi-period returns are products of the returns in each period

Annualized return, based on monthly return

Continuously compounded returns, where is the simple return:

Taking the exponential of both sides yields

Converting between continuously compounded returns and simple returns is (rearranging the above)

For continuously compounded returns, the continuously compounded multi-period returns is just the sum of the continuously compounded return for each period (which makes it easier to calculate than the simple return):