AMS-Theory of Interest

Project Guidelines: Answer both questions in a well written document. It should be presented in a way such that someone unfamiliar with AMS 318 can gain something from reading your report. Include graphs and tables when appropriate to succinctly describe results and data. This is a test of your mathematical and communication skills. Do not just write every equation. 1. In the spreadsheet for [login to view URL] you will nd the specications for two projects. This includes how much will be received or invested and at which time. Some of the values are unknown, specically X; t1; t2; t3. Investigate what values for these variables will make project 2 preferable to project 1. You may impose restrictions on your variables to attain closed form solutions if you like. Assume money is earned at the compound interest rate given in the spreadsheet. NO.2 is in the attach file. one more bonus question:You will likely need to use a programming language to complete this bonus problem, check it out below: You are given a unique investment opportunity. Starting with $1 of capital, you can choose a fixed proportion, f, of your capital to bet on a fair coin toss repeatedly for 1000 tosses. Your return is double your bet for heads and you lose your bet for tails. For example, if f  = 1/4, for the first toss you bet $0.25, and if heads comes up you win $0.5 and so then have $1.5. You then bet $0.375 and if the second toss is tails, you have $1.125. Choosing f to maximize your chances of having at least $1,000,000,000 after 1,000 flips, what is the chance that you become a billionaire? All computations are assumed to be exact (no rounding), but give your answer rounded to 12 digits behind the decimal point in the form 0.abcdefghijkl.