Question 1209145
**1. Determine Edison's 18th Birthday**

* **Birthdate:** Thomas Edison was born on February 11, 1847.
* **18th Birthday:** February 11, 1865.

**2. Calculate the Number of Years (t)**

* **Current Year:** 2024
* **Years Since Investment:** 2024 - 1865 = 159 years

**3. Calculate the Number of Compounding Periods (n)**

* **Compounding Frequency:** Hourly 
* **Hours in a Year:** 24 hours/day * 365 days/year = 8760 hours/year
* **Total Compounding Periods:** 159 years * 8760 hours/year = 1,392,240 periods 

**4. Calculate the Interest Rate per Period (r)**

* **Annual Interest Rate:** 0.8% = 0.008
* **Interest Rate per Hour:** 0.008 / 8760 hours/year ≈ 9.116 x 10^-7 

**5. Calculate the Future Value (A)**

* **Formula for Compound Interest:** A = P(1 + r/n)^(n*t) 
    * Where:
        * A = Future Value
        * P = Principal ($200,000)
        * r = Interest Rate per Period
        * n = Number of Compounding Periods
        * t = Number of Years

* **Calculation:** 
    * A = $200,000 * (1 + 9.116 x 10^-7)^(1,392,240)
    * A ≈ $200,000 * 2.902 
    * A ≈ $580,400

**Therefore, if Thomas Edison had invested $200,000 at 0.8% compounded hourly on his 18th birthday, the account would have approximately $580,400 in 2024.**

**Explanation:**

* We first determined Edison's 18th birthday to calculate the number of years the investment has been compounding. 
* Since the interest is compounded hourly, we calculated the number of compounding periods by multiplying the number of years by the number of hours in a year. 
* We then calculated the hourly interest rate by dividing the annual interest rate by the number of hours in a year. 
* Finally, we used the compound interest formula to calculate the future value of the investment.

**Note:** This calculation assumes a constant interest rate throughout the entire period, which may not be entirely accurate in reality.