Elevation Mining has seen steady growth over the past several years and demand is expected to rise in the coming years. Management knows that they must have competitive solutions to transport their commodities from mines to railways, ports, ships, and their destination markets. The company is looking to develop solutions that increase supply chain efficiency and accountability. They have decided to set aside $$3,000,000$ to fund the expansion and improvement of their logistical services. Management has developed two different options for expansion over the next four years. The first option would require equal amounts of $$800,000$ to be available at the end of each of the next four years. The second option would require $$400,000$ now, $$850,000$ one year from now, $$900,000$ three years from now and $$1,000,000$ four years from now. The $$3,000,000$ will be invested throughout the process to fund the accepted option. They have secured progressive rates of $4\mathrm{.}00\%$ compounded semiannually for the first year, $4\mathrm{.}60\%$ compounded semiannually for the second year and $5\mathrm{.}00\%$ compounded semiannually for the remaining two years.

$3.$ Would the funds invested be sufficient to fund the second option presented? Determine the current value of the payments required in your analysis. Include a time diagram as part of your complete solution. $[7$ marks$]$

$4.$ What is the difference between the cash required for the second option and the cash available from the investment? $[1$ mark$]$

$5.$ Based on your financial analysis, which option would you suggest to Elevation Mining? Explain. $[2$ marks$]$

$6.$ Repeat your analysis for each option if the company instead decides to invest the $$3,000,000$ in a fund that provides $4\mathrm{.}80\%$ compounded quarterly. Include time diagrams as part of your complete solution. Based on your financial analysis, which option would you suggest to Elevation Mining? Explain. $[10$ marks$]$

$7.$ Is it better for Elevation mining to choose the progressive rates or the fixed rate option? Explain. $[2]$