I have been asked to create a formula for the duration, 'd' of a continuously compounding investment for the time interval 0 <= t <= T.
I know that the 'force of interest' $\delta$ = ln(1+i), which means that $(1+i)^t$ = e^$\delta$t.
I also know that in order to create this formula, we will need to remove the summation signs and replace them with integrals, and the series of payments will be replaced with a function p(t).
From these basic ideas, I am at a loss of where to go next. I would definitely appreciate some more explanation and a push in the right direction.
Thanks!
One way to go would be to solve the integral directly and have a closed form formula for your function. $e^{-\delta t}$ usually integrates very well :) (with $t e^{-\delta t}$ usually integrating by parts!)