Question

You plan on depositing $6,000 at the end of each year for 40 years into a retirement account that pays 4% interest. How much could you withdraw annually in equal beginning of year amounts starting at the time you make your last deposit and continuing for a total of 20 years, assuming balances continue to earn 4% until withdrawn?

Answer 1

Answer :

We know that,

Future value of annuity = P * [ ( 1 + r )^n - 1 / i ]

Where, P = 6,000

r = 4% (or) 0.04

n = 40

Then,

Future value of annuity = 6,000 * [ ( 1 + 0.04 )^40 - 1 / 0.04 ]

= 6,000 * [ ( 1.04 )^40 - 1 / 0.04 ]

= 570,153.10

Therefore,

Amount that can be withdrawn annually = P * r * ( 1 + r )^n / ( 1 + r )^n - 1

Where, P = 570,153.10 and r = 0.04 and n = 20

= 570,153.10 * 0.04 * ( 1 + 0.04 )^20 / ( 1 + 0.04 )^20 - 1

= 570,153.10 * 0.04 * 1.04^20 / 1.04^20 - 1

= 41,952.86