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.
