An investor wishes to borrow $37000$ from a bank at an effective rate of interest of $7\mathrm{.}2\%$ per annum to finance the expansion of his business. The project is expected to generate net revenues of $3840$ per annum payable monthly in arrears for the next $19$ years.

$($a$)$ Find the discounted payback period for this project $($in whole months$)$

$($b$)$ Once the loan has been repaid, the investor can earn $2\mathrm{.}5\%$ per annum convertible monthly on investing the revenues received. Making use of the result from part $($a$),$ find the total profit that the investor will make at the end of the $19-$year investment project.