Question 1200973
Certainly, let's calculate the required initial deposit for Carter's retirement account.

**Understanding the Scenario**

* **Annual Withdrawal:** $120,000
* **Interest Rate:** 5% per year
* **Retirement Years:** 30 years
* **Interest Payment Start:** One year after retirement

**Calculation**

Since the interest starts paying one year after retirement, we can use the formula for the present value of an ordinary annuity:

* **Present Value of Annuity = Annual Withdrawal * [(1 - (1 + Interest Rate)^(-Number of Years)) / Interest Rate]**

Substituting the values:

* Present Value of Annuity = $120,000 * [(1 - (1 + 0.05)^(-30)) / 0.05]
* Present Value of Annuity = $120,000 * [(1 - 0.231377) / 0.05]
* Present Value of Annuity = $120,000 * [0.768623 / 0.05]
* Present Value of Annuity = $120,000 * 15.37246
* Present Value of Annuity = $1,844,694.12

**Therefore, Carter will need to deposit $1,844,694.12 at the beginning of his retirement to cover his living expenses for 30 years.**

Let me know if you have any other questions or would like to explore different scenarios!