Enter your capitalization/discounting (\(f(t)\)) function and compute the or force of interest (\(\delta(t)\)) or viceversa.
How to write a proper function:
\(2t+5 \;\Rightarrow \;\) 2*t+5
\( \frac{1}{1+t} \;\Rightarrow \;\) 1/(1+t)
\(t^2 \;\Rightarrow \;\) t^2
\(t^{-2} \;\Rightarrow \;\) t^(-2)
\((1+ir)^{t+1} \;\Rightarrow \;\) (1+ir)^(t+1)
\( \sqrt{1+t} \;\Rightarrow \;\) (1+t)^(1/2)
\( e^{-0.2t} \;\Rightarrow \;\) exp(-0.2*t)
THEORY - THE IDEA OF THE STEPS
if you have the function \( f(t) \)
\[ \delta(t) = \frac{ f'(t) }{ f(t) } \]
First compute the first derivative of the function, then divide it by the initial function.
if you have the force of inerest \( \delta(t) \)
\[ f(t) \;=\; e^{ \int_0^t \delta (t) dt } \]
First compute the integral from \(0\) to \(t\) of the force of interest, then take its exponential.