Its Erin's 30^th birthday. She has decided that it is necessary to plan her own retirement since she not sure that government benefits will be available when she retires. She will make annual payments into an account earning 4% APY starting on her next birthday (31^st) a year from now. Her last payment will occur on her 70^th birthday. She has decided that she needs to plan for payments of $400,000 per year and that there will be a total of 20 yearly payments made starting on her 70^th birthday.

- How much should be in her account on her 70^th birthday in order to accomplish this goal?

- How much will her annual payment until she retire need to be in order to accomplish this goal?

- Suppose this is her 45^th birthday, instead of her 30^th birthday in the problem above. Now, how much will her annual payment until she retires needs to be in order to accomplish her goal?