B27 Continuous Anuities

Question 1

what is the PV of an annuity whose pmts are at a rate of f(t) and a non constant force of interest at δ_t?

Answer 1

PV = ∫ from 0 to n (f(t) * e^(∫ from 0 to t (δ_s)) dt

Question 2

what is the AV of an annuity whose pmts are at a rate of f(t) and a non constant force of interest at δ_t?

Answer 2

AV = ∫ from 0 to n (f(t) * e^(∫ from t to n (δ_s)) dt