You Have $100,000 That You Want to Invest $\sum_{i=1}^{365} 200(365) e^{\frac{0.05}{365} t_{i}} \Delta t$

question 35

Multiple Choice

You have $100,000 that you want to invest.Some "business men" are willing to sell you a machine for your $100,000 that prints money.You figure that every day you can print $200 with the machine, and you would deposit the $200 each day in a "special" bank account at BCCI.Your friends at BCCI will only be able to offer you 5% nominal annual interest, compounded continuously, due to the "sensitive nature" of the transaction.It would be your intention to print money each day for one year.Which of the following sums gives the value of your bank balance after one year?

• A) \(\sum_{i=1}^{365} 200(365) e^{\frac{0.05}{365} t_{i}} \Delta t\) , with \(\Delta t=1\) day
• B) \(\sum_{i=1}^{365} 200\left(e^{\frac{0.05}{365}\left(365-t_{i}\right)}-1\right) \Delta t\) , with \(\Delta t=1\) day
• C) \(\sum_{i=1}^{365} 200 e^{\frac{0.05}{365}}\left(365-t_{i}\right) \Delta t\)
• , with \(\Delta t=1\) day
• D) \(\sum_{i=1}^{365} 200\left(e^{\frac{0.05}{365} t_{i}}-1\right) \Delta t\) , with \(\Delta t=1\) day

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Definitions:

Fluoride

A mineral used in dental care to strengthen tooth enamel and prevent cavities, often added to toothpaste, mouthwash, and some public water supplies.

Drinking Water

H2O that is safe and suitable for human consumption, free from contaminants and pathogens.

Health Promotion

The process of enabling people to increase control over, and to improve, their health through lifestyle changes and societal interventions.

External Variables

Factors outside the control of an individual or study that can influence outcomes or behaviors.