Question

You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal

Answer 1

You need to have $904,510.28 in your account when you begin

Answer 2

$904,510.28

Explanation:

If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.

P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)

where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.

Filling in your values, we have ...

P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)

P = $904,510.28

You need to have $904,510.28 in your account when you begin withdrawals.