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

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