You own a 50,000 shares in XYZ Corporation. The current price of XYZ is S₀ = 35 and the stocks price is lognormally distributed with mean = 25% and standard deviation = 50%. The Togo Bank has given you a loan of $2,000,000. The loan conditions are:

Loan term: 10 years. The loan is a bullet loan, meaning that there is no payment of interest or principal until year 10.

Loan interest: 8% annually. In year 10 you will owe Togo Bank $2,000,000*(1.08)¹⁰ .

The loan is a non-recourse loan, secured only by your stock package. This means that if the final payment on the loan is more than the value in year 10 of the shares, Star Bank will get the package of stocks.

You are asked:

1. To simulate one path of the stock price and to compute the rate of return on the loan to the bank.
2. To simulate 25 possible outcomes to compute Togo Banks expected rate of return and the standard deviation of this return.