Hotseat Q.pdf (0,3 MB)
Hello, my answer is in the attached PDF. I assumed that by "simple continuous payment" you meant a continuously payable annuity (where the payment stream is constant throughout the term of the annuity).
The formulae are the same, however for a continuously payable annuity, p(t) = 1, because the rate of payment is constant (neither increasing nor decreasing).
If this wasn't what you meant please comment further on this answer.