dear professor,
Why is the temporary complete life expectancy not just the integral with respect to t between 0 and n of the function t*t_p_x*mu_x+t, which, integrating by parts, becomes minus n*n_p_x plus the integral with respect to t between 0 and n of the function t_p_x? In the text books, n*n_p_x is added to this, resulting in the integral with respect to t between 0 and n of the function t_p_x. What is the reason for this addition? Surely it is not just so that it becomes conveniently numerically equal to the EPV of a temporary continuous life annuity where delta (the interest rate) is equal to 0.