AMS-Theory of Interest

This project was awarded to raiseq for $120 USD.

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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 [url removed, login to view] 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 $[url removed, login to view], and if heads comes up you win $0.5 and so then have $1.5. You then bet $[url removed, login to view] 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.

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