11. Zoe has been depositing $900 every month into her retirement account for 35 years. The annual interest rate in this account is guaranteed for life to be 4.5%, and the interest is compounded monthly. Now, Zoe is retiring. She plans to live off her pension for 20 more years. a) how much money can she withdraw from the account every month so that the account is depleted exactly in 20 years? Write the formula in the box below ( 900 (1+0.00 375) 420. 0.00375 Write the answer in the box below 915967.76 (b) how much money could she withdraw every month if she planned to live off the pension for 25 more years instead? Write the answer in the box below 5,091.25 (c) suppose Zoe plans to live for 25 more years, and draws her pension money accordingly, but dies after 20 years; how much money will be left in the account after her death?
11. Zoe has been depositing $900 every month into her retirement account for 35 years. The annual interest rate in this account is guaranteed for life to be 4.5%, and the interest is compounded monthly. Now, Zoe is retiring. She plans to live off her pension for 20 more years. a) how much money can she withdraw from the account every month so that the account is depleted exactly in 20 years? Write the formula in the box below ( 900 (1+0.00 375) 420. 0.00375 Write the answer in the box below 915967.76 (b) how much money could she withdraw every month if she planned to live off the pension for 25 more years instead? Write the answer in the box below 5,091.25 (c) suppose Zoe plans to live for 25 more years, and draws her pension money accordingly, but dies after 20 years; how much money will be left in the account after her death?
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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![### Problem 11
Zoe has been depositing $900 every month into her retirement account for 35 years. The annual interest rate in this account is guaranteed for life to be 4.5%, and the interest is compounded monthly. Now, Zoe is retiring and plans to withdraw from this account over 20 or 25 years.
#### (a) Retirement Plan for 20 Years
Calculate the monthly withdrawal amount so that the account is depleted in exactly 20 years.
**Formula Used:**
\[ 900 \left(\frac{(1 + 0.00375)^{420} - 1}{0.00375}\right) \]
**Answer:**
$915,867.76
#### (b) Retirement Plan for 25 Years
Calculate the monthly withdrawal amount if Zoe plans to live off the pension for 25 years.
**Answer:**
$5,091.25
#### (c) Early Withdrawal Plan
Suppose Zoe plans to live for 25 more years and makes withdrawals accordingly, but she passes away after 20 years. Calculate how much money will be left in the account after her death.
**Formula Used:**
*(The formula box is empty)*
**Answer:**
*(The answer box is empty)*
---
### Explanation:
1. **Interest Rate and Compounding:** The problem involves calculating future values and withdrawal strategies based on a fixed annual interest rate of 4.5% compounded monthly. This translates to a monthly interest rate of 0.00375 (or 0.375%).
2. **20-Year Withdrawal Plan:** The formula calculates the future value of the monthly deposits compounded monthly for 420 months (35 years). It estimates how much can be withdrawn monthly over 240 months (20 years).
3. **25-Year Withdrawal Plan:** This requires determining the withdrawal amount for 300 months (25 years), adjusting for the longer period without additional inflow from deposits.
4. **Remaining Balance After 20 Years:** This section appears incomplete, inviting the calculation of residual balance if withdrawals are structured over 25 years, but life expectancy falls to 20 years. This involves recalculating based on the adjusted withdrawal strategy.
This exercise helps understand savings growth, retirement planning, and compound interest dynamics over extended periods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c7d557f-b8ce-455f-9604-6b1b708172f0%2F1611e8a6-7d07-43b1-af2e-776ae709fcc0%2F9xzaggd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 11
Zoe has been depositing $900 every month into her retirement account for 35 years. The annual interest rate in this account is guaranteed for life to be 4.5%, and the interest is compounded monthly. Now, Zoe is retiring and plans to withdraw from this account over 20 or 25 years.
#### (a) Retirement Plan for 20 Years
Calculate the monthly withdrawal amount so that the account is depleted in exactly 20 years.
**Formula Used:**
\[ 900 \left(\frac{(1 + 0.00375)^{420} - 1}{0.00375}\right) \]
**Answer:**
$915,867.76
#### (b) Retirement Plan for 25 Years
Calculate the monthly withdrawal amount if Zoe plans to live off the pension for 25 years.
**Answer:**
$5,091.25
#### (c) Early Withdrawal Plan
Suppose Zoe plans to live for 25 more years and makes withdrawals accordingly, but she passes away after 20 years. Calculate how much money will be left in the account after her death.
**Formula Used:**
*(The formula box is empty)*
**Answer:**
*(The answer box is empty)*
---
### Explanation:
1. **Interest Rate and Compounding:** The problem involves calculating future values and withdrawal strategies based on a fixed annual interest rate of 4.5% compounded monthly. This translates to a monthly interest rate of 0.00375 (or 0.375%).
2. **20-Year Withdrawal Plan:** The formula calculates the future value of the monthly deposits compounded monthly for 420 months (35 years). It estimates how much can be withdrawn monthly over 240 months (20 years).
3. **25-Year Withdrawal Plan:** This requires determining the withdrawal amount for 300 months (25 years), adjusting for the longer period without additional inflow from deposits.
4. **Remaining Balance After 20 Years:** This section appears incomplete, inviting the calculation of residual balance if withdrawals are structured over 25 years, but life expectancy falls to 20 years. This involves recalculating based on the adjusted withdrawal strategy.
This exercise helps understand savings growth, retirement planning, and compound interest dynamics over extended periods.
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