Answer: you need to have at least $312,500 in your account at the beginning.
Explanation:
The total amount of money you will need to withdraw over the 25-year period is $30,000 * 25 years = $750,000. To find the total amount of interest you will earn, we need to use a compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^nt
where A is the total amount of money you will have in your account after 25 years, P is the initial amount of money in your account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In our case, we have A = $750,000, P = ?, r = 8%, n = 1 (since the interest is compounded annually), and t = 25. Plugging these values into the formula, we get:
$750,000 = P * (1 + 0.08/1)^1 * 25
We can simplify this equation to:
$750,000 = P * 1.08^25
To find the value of P, we can divide both sides of the equation by 1.08^25:
$750,000 / 1.08^25 = P
We can use a calculator to compute the value of 1.08^25, which is approximately 2.4. This means that the initial amount of money you need in your account is $750,000 / 2.4 = $312,500.
Therefore, to be able to withdraw $30,000 each year for 25 years and earn 8% interest on your account, you need to have at least $312,500 in your account at the beginning.