Answer :

Answer:

  $205,473.08

Step-by-step explanation:

You want to know the present value of a 30-year annuity that earns 9% compounded annually and provides a payment of $20,000 each year.

Ordinary annuity

Assuming the withdrawal comes at the end of the year, the value of the ordinary annuity is ...

  A = P(1 -(1 +r)^-n)/r

where P is the annual payment, r is the interest rate, and n is the number of years.

Here, we have ...

  A = 20000(1 -(1.09^-30))/0.09 ≈ 205,473.08

Jake needs to invest $205,473.08 to support his withdrawals.

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Additional comment

If Jake's first withdrawal is coincident with his investment, then the arrangement is called an annuity due. The amount needed is 9% more.

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