Question

Suppose you have $1,500,000 when you retire and want to withdraw an equal amount each year for the next 30 years. How much would you be able to withdraw each year if the market failed and your earnings dropped to -.5%? How long would it take to drain your account if you did nothing about this loss pattern?

How can we solve this manually? (No excel) Please explain.

Answer 1

We first calculate how muchyou can withdraw each year which is the annuity

Here we have PV = 1,500,000

n =30 and r = -0.005 =-0.5%

The PV of an annuity = P*(1-(1+r)^-n)/r

1,500,000 = P*(1-(1-0.005)^-30)/(-0.005)

1,500,000 = P*(-0.16227147)/(-0.005)

On solving, we get P = 46,218.85

So, you will be able to withdraw $46,218.85 annually for 30 years if the earnings drop by -0.5% each year.

If you withdraw 46,218.85 for 30 years and you get a rate of -0.5% loss each year. You would drain all of your earnings in 30 years. However, if you withdraw a larger a mount you would drain your account earlier. To calculate how long it takes to drain the account, we need to know the amount that you withdraw each year.