I am 25 year old. I want to retire on my 70th birthday (35 years of working) with an annual income (taken out of my retirement savings at the beginning of each year) of $100,000 at today's prices.

I think that the return I will earn on my retirement savings while in retirement is 3% Effective Annual Rate (EAR) in real terms. I will probably live till I am 90 years old. (21 years of retirement) and I hope to leave $100,000 (at today's prices) for my kids on my 91st birthday. I like to plan ahead, haha.

a. Can you please help me determine the amount (at today's prices) that I will need to have accumulated in my retirement account by retirement to be able to fund my retirement spending.

i. What is the value of this amount at retirement (my 70th birthday) at today's prices?

ii. What would the amount be on my 70th birthday if I thought instead that I would live to the end of my 95th year (26 years of retirement)?

iii. What would the amount be if I thought I would live to the end of my 95th year and my return was only going to be 2% (EAR) in real terms during retirement?

iv. What would the amount be if I thought I would live to the end of their 95th year, my return was only going to be 2% (EAR) in real terms, and if I assumed (realistically) that I would see a 30% tax rate on my annual withdrawals (not including the final distribution to the kids)?

b. Pretty please find out the real amount (at today's prices) I would need to save each year in order accumulate this retirement account amount (part a.i.). Assume that over my working life I will invest the funds at the end of each year. Assume that I also believe I will earn a return of 5% (EAR) in real terms.

i. What would the annual amount be (at today's prices) given the retirement account balance required in part a(i) assuming I started contributing at the end of the year following my 25th birthday?

ii. Given this same required retirement account balance (a.i.) assumptions), what would the annual amount be assuming the return I earned was only expected to be 4% (EAR) in real terms?

iii. Given this retirement account balance (a.i. assumptions), what would the annual amount be assuming I waited and started contributing at age 35? (return EAR to 5%)?