You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 74 years from now. What is the present value of your windfall if the appropriate discount rate is 9 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value
You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 74 years from now. What is the present value of your windfall if the appropriate discount rate is 9 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Exploring Present Value Calculations in Financial Mathematics**
In this exercise, you have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, which is 74 years from now. To determine the present value of this prize, we need to calculate it using a discount rate of 9 percent.
**Problem Statement:**
- **Given:** $1 million prize, awarded in 74 years.
- **Discount Rate:** 9 percent.
- **Task:** Find the present value.
**Steps to Calculate Present Value:**
1. **Formula for Present Value (PV):**
\[ PV = \frac{FV}{(1 + r)^n} \]
- \(PV\): Present Value
- \(FV\): Future Value (\$1,000,000 in this case)
- \(r\): Discount rate (0.09 for 9 percent)
- \(n\): Number of periods (74 years)
2. **Plugging in the Values:**
\[ PV = \frac{1,000,000}{(1 + 0.09)^{74}} \]
3. **Intermediate Calculations:**
- Calculate \( (1 + 0.09)^{74} \) without rounding intermediate values.
- Divide the Future Value by the calculated amount.
4. **Final Answer:**
- Round the answer to 2 decimal places to get the present value.
**Visual Aid:**
_Typically, a graph could illustrate the exponential growth of money over time using the formula above, showing the rapid increase in the amount needed due to the high discount rate over a long period._
_No visual graphs or diagrams are provided in this particular exercise; the focus is on the textual calculation._
**Calculation Interface:**
- A textbox is provided for entering the present value after performing the calculations:
```Present value: [_____________]```
By working through this exercise, you’ll gain a better understanding of the impact of time and interest rates on the value of money, a key concept in financial mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd87d8eee-b792-430e-98e8-ed118dd425ec%2F4624473f-3065-417d-8772-08707c821d0d%2Fkz56y8h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exploring Present Value Calculations in Financial Mathematics**
In this exercise, you have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, which is 74 years from now. To determine the present value of this prize, we need to calculate it using a discount rate of 9 percent.
**Problem Statement:**
- **Given:** $1 million prize, awarded in 74 years.
- **Discount Rate:** 9 percent.
- **Task:** Find the present value.
**Steps to Calculate Present Value:**
1. **Formula for Present Value (PV):**
\[ PV = \frac{FV}{(1 + r)^n} \]
- \(PV\): Present Value
- \(FV\): Future Value (\$1,000,000 in this case)
- \(r\): Discount rate (0.09 for 9 percent)
- \(n\): Number of periods (74 years)
2. **Plugging in the Values:**
\[ PV = \frac{1,000,000}{(1 + 0.09)^{74}} \]
3. **Intermediate Calculations:**
- Calculate \( (1 + 0.09)^{74} \) without rounding intermediate values.
- Divide the Future Value by the calculated amount.
4. **Final Answer:**
- Round the answer to 2 decimal places to get the present value.
**Visual Aid:**
_Typically, a graph could illustrate the exponential growth of money over time using the formula above, showing the rapid increase in the amount needed due to the high discount rate over a long period._
_No visual graphs or diagrams are provided in this particular exercise; the focus is on the textual calculation._
**Calculation Interface:**
- A textbox is provided for entering the present value after performing the calculations:
```Present value: [_____________]```
By working through this exercise, you’ll gain a better understanding of the impact of time and interest rates on the value of money, a key concept in financial mathematics.
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