Question 1200973: Carter expects to live for 30 years more after his retirement. He would like to withdraw $120,000 every year from his investment account (Account A) to pay for his living expenses. Carter’s investment account (Account A) pays 5% interest per year.
How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60) to pay for his living expenses if
(i) Account A start to pay interest one year after his retirement?
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! 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!
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