Question

suppose you are35 years old and would like to retire at age65 . ​Furthermore, you would like to have a retirement fund from which you can draw an income of ​$150000 per year​forever! How much would you need to deposit each month to do​ this? Assume a constant APR of8 ​% and that the compounding and payment periods are the same.

Answer 1

$1258.09

Explanation:

You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.

Account balance

In order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.

I = Prt

150,000 = P(0.08)(1)

P = 150,000/0.08 = 1,875,000

Annuity payment

The value of an ordinary annuity is given by the formula ...

A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.

Using the values we know, we can find P:

1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P

P ≈ 1258.09

You would need to deposit $1258.09 each month.

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Additional comment

The formulas used here assume that the deposits and withdrawals occur at the end of the month.