Question 1209145: The year he turned 18, Thomas Edison invested $200,000 at 0.8% compounded hourly. How much money would the account have now? Explain all steps. Be sure to include an explanation of how you found out when Edison turned 18 and how you calculated n. Part of the credit is for your explanation. It should be thorough.
1. How much money would be in the account now in 2024 at 0.8% compounded hourly.
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **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.
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