The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate the PV for each of the following cases.

The annuity payments arrive at one-year intervals. The first payment arrives one year from now.

The first payment arrives in six months. Following payments arrive at one-year intervals (i.e., and 18 months, 30 months, etc)