Assume the force of interest function is as follows:

t={0.04, 0t6,

0.05, 6t12)

where time t is measured in years. (a) An annuity pays continuously at a rate of 150 + 10t per year for 5 years. Find the present value of this annuity. (b) An annuity pays continuously at a rate of 150 + 10t per year for 10 years. Find the present value of this annuity.