NOTE$-$ please use BMAT compound interest methods to solve

Max's second investment was a $\backslash (\backslash$$ $6500\backslash )$ venture into a series of T$-$notes that will mature $12$ years and $9$ months after inception.

d$)$ What nominal rate, compounded monthly, will allow the T$-$notes to double in value during this period of time? $(4$ marks$)$

Through loans, pulling investments, credit cards, and borrowing from friends and family, Max has raised enough capital to start his business on the right foot. However, Max's financial knowledge and budgeting skills make him aware that his company will be $\backslash$$$64,500$ in debt $6$ months from now, with that debt growing at $\backslash (4\backslash \%\backslash )$ compounded quarterly.

Because Max's business is cyclical, his revenue comes in big chunks rather than an equal amount every month. Max estimates he will be able to make payments towards his debt in $15$ months, $28$ months, and $50$ months.

e$)$ Max wishes to be debt$-$free after the last payment and decides to make payments of equal size at the planned times. How large should these payments be$?$ Include a detailed timeline. Use $6$ months as the focal date. $(8$ marks$)$