Question

You are 45 years old and planning to retire at age 65. You expect to live until age 85. Your retirment investment earns 9% per year. You want to guarentee that you will withdrawl 15000 per month during retiremnent. You expect that inflation will be 3% per year including years in retirement. How much must you save per month until retirment to fund your plan. HINT: Your retirment withdrawl will increase every month at the inflation rate of 3%. The payments will not be the same every month. This means you need to project each month's retirment withdrawl and use the NPV function to find the present value of all of the payments. Project the monthly withdrqawls out to the right and use monthly compounding for the inflation to make the calculation easier. Your first withdrawl will not be 15000. It will be more.  

Answer 1

1$ at 0.4988% per month after 240 monts (20 years*12) will be
FV = P * {(((1+R)^N) - 1) / R}
FV=1*((((1+.4988%)^240)-1)/.4988%)
Real FV of 1$ invested every month after 20 years					461.25
Present Value of the 15000 in real term monthly
15000=(x*0.4988%*(1+.4988%)^240)/((1+0.4988%)^240-1)
x=15000*((1+0.4988%)^240-1)/(0.4988%*(1+0.4988%)^240)					2,096,141
Every month money is required to be invested=2096141/461.25					4,544.48
Working Note:
Calculation of monthly real rate of return
Real rate of Return=((1+nominal Rate)/(1+inflation rate))-1
Monthly Nominal Rate of return=9/12=0.75%
Monthly Inflation Rate =3/12=0.25%
Real rate of return=((1+0.75%)/(1+0.25%))-1					0.4988%