If you want to be able to withdraw $100,000 per year forever beginning 20 years from now, how much will you have to have in your retirement account (that earns 8% per year interest) in year 0 (now)

The answer is $289,640.08

Explanation:

Solution

Given that:

You want to make a withdrawal of the amount = $100,000 per year

Number of years = 20

Interest per year = 8%

Now,

Let the current balance required is X

The amount in bank due to the interest after 19 years = X (1+0.08) ^19

This should be equal to the 100,000 drawn forever.

Thus,

X (1.08) 20-100,000=A (1.08) 19 [i. e after drawing $100,000 a year later, this same amount should remain]

Hence,

X = $289,640.08

Therefore the amount you will have to have in your retirement account in year 0 is $289,640.08