A cash flow is payable continuously at a rate of t per annum at time t provided a life who is aged x at time 0 is still alive. Tx is a random variable which measures the complete future lifetime in years of a life aged x. i) Write down an expression, in terms of Tx, for the present value at time 0 of this cash flow using a constant force of interest of per annum. ii) Hence or otherwise, show that the expected present value at time 0 of this cash flow is equal to: 0ex(s)spxds A cash flow is payable continuously at a rate of t per annum at time t provided a life who is aged x at time 0 is still alive. Tx is a random variable which measures the complete future lifetime in years of a life aged x. i) Write down an expression, in terms of Tx, for the present value at time 0 of this cash flow using a constant force of interest of per annum. ii) Hence or otherwise, show that the expected present value at time 0 of this cash flow is equal to: 0ex(s)spxds