Assignments Grades People Syllabus Modules Google Drive Office 365 You want to be able to withdraw $\$ 20,000$ each year for 15 years. Your account earns $10 \%$ interest. 18 a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? $\$$ c) How much of that money is interest?

Step 1 ：We are given that the annual withdrawal amount is $20,000 for 15 years, and the account earns an interest of 10% per annum. We are to find the initial amount needed in the account, the total amount withdrawn, and the total interest earned.

Step 2 ：First, we calculate the total amount that will be withdrawn over the 15 years. This is simply the annual withdrawal amount multiplied by the number of years, which is $20,000 * 15 = $300,000.

Step 3 ：Next, we need to find the initial amount needed in the account. This is the present value (PV) of the total amount to be withdrawn. We can find this using the formula for the present value of an annuity: \(PV = \frac{FV}{(1 + r)^n}\), where FV is the future value of the annuity, r is the interest rate per period, and n is the number of periods.

Step 4 ：Substituting the given values into the formula, we get \(PV = \frac{300000}{(1 + 0.1)^{15}}\).

Step 5 ：Solving this equation gives us the initial amount needed in the account, which is approximately $71,817.61.

Step 6 ：Finally, we calculate the total interest earned. This is simply the total amount withdrawn minus the initial amount in the account, which is $300,000 - $71,817.61 = $228,182.39.

Step 7 ：\(\boxed{\text{Final Answer:}}\) You need to have approximately \(\boxed{\$71,817.61}\) in your account at the beginning. The total amount you will withdraw is \(\boxed{\$300,000}\), and the total interest earned is \(\boxed{\$228,182.39}\).