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You just won the lottery! You wish to put enough money away so that you can...

You just won the lottery! You wish to put enough money away so that you can withdraw $3,000 monthly for 20 years. You can earn 8% rate on any funds you deposit. How much will you have to deposit now to meet your goal? (Note: Compounding matches the withdrawal frequency.)

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Answer #1
This can be solved using Present value of annuity formula
Present value of annuity is = P*(1-(1+r)^-n)/r
"P" Monthly withdraw = $ 3,000/.
"r" is Monthly interest rate = 8%/12 = 0.67%
"n" is No of months = 20*12 = 240
Present value of annuity is = Deposit now to meet your goal
Present value is = 3000*(1-(1+0.0067)^-240)/0.0067
Present value is = 3000*119.19929
Present value is = $ 357,597.86/.
You have to deposit now $ 357,597.86/. Approx.
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