54.5k views
4 votes
You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest.

a. How much do you need in your account at the beginning

1 Answer

3 votes

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.

User Chris Crewdson
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.