In the present value expression for a life policy with constant μ and δ, delta represents which concept?

• A. The force of interest
• B. The force of mortality
• C. The discount rate per period
• D. The probability of survival

Answer: (A)

Delta is the force of interest—the instantaneous rate at which money grows (or discounts) in continuous time. In a present value expression with a constant delta, a payment at time t is valued today by multiplying by e^{-δ t}, which represents continuous compounding. The mortality intensity μ governs survival, with a constant μ giving a survival function S(t) = e^{-μ t}, so it affects who is alive to receive benefit, not how we discount cash flows. The discrete discount rate (often denoted i or d) uses different compounding, not the continuous δ, reinforcing that delta specifically captures continuous-time discounting.