Question

Assume you earned 9% per year on your portfolio instead of 8% during the 40 yrs you were saving for retirement. if your annual saving was the amount found of 12,399, how much money would you be able to live on in retirement each year assuming you live to age 100? Assuming you can earn 5% in retirement and pay yourself at the beginning of each year. show work.. age 25, retirement 65

Answer 1

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Assumed Annual deposits are period end deposits.

Particulars	Amount
Cash Flow	$          12,399.00
Int Rate	9.000%
Periods	40

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 12399 * [ [ ( 1 + 0.09 ) ^ 40 ] - 1 ] / 0.09
= $ 12399 * [ [ ( 1.09 ) ^ 40 ] - 1 ] / 0.09
= $ 12399 * [ [31.4094] - 1 ] / 0.09
= $ 12399 * [30.4094] /0.09
= $ 4189404.44

Amount that can be with drawn during retirement:

Given Withdrawla are made at the begining of the period.

PV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the begining of the period.PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period
n - No. of periods

Cash Flow = PV of Annuity Due / [ 1 + PVAF (r%, n - 1 ) ]  
= $ 4189404.44 / [ 1 + PVAF ( 5%, 35 - 1 ) ]  
= $ 4189404.44 / [ 1 + 16.1929 ]  
= $ 4189404.44 / [ 17.1929 ]  
= $ 243670.55  

Annual Cash withdrawl is $ 243670.55