Which expression gives nyearterm, the n-year term annuity under constant force of mortality?

• A. (mu+delta)*(1 - nEx)
• B. (1 - nEx)/mu
• C. (1/mu)*(1 - nEx)
• D. (1/(mu+delta))*(1 - nEx)

Answer: (D)

For a unit payment stream of length n, paid at the end of each year while the life is alive, with mortality modeled by a constant force μ and discounting at a constant force δ, the value depends on the combined effect of survival and time value. The probability of surviving to n years is nEx = e^{-μ n}, and the discounting introduces the factor e^{-δ t} for time t. Under these constant forces, the present value of the nyearterm annuity can be expressed compactly as the total time-value-adjusted survival over the horizon, which yields (1/(μ+δ)) times (1 − nEx). Since nEx = e^{-μ n}, this matches the familiar form (1/(μ+δ))(1 − e^{-μ n}).

Thus the nyearterm value is best given by the expression (1/(μ+δ)) (1 − nEx).