An investment plan is to incur an initial cost of $$4\mathrm{.}2$ million at the outset and additional costs

continuously at the rate of $$1\mathrm{.}5$ million per year in the first $3$ years. After that it is expected

to deliver net profits of $2\mathrm{.}7$ million at the end of each year from years $4$ to $10.$

The effective annual borrowing rate is $9\%$ on negative accumulated profit and the effective

annual lending rate is $7\mathrm{.}5\%$ on positive accumulated profit.

$($a$)$ Find the internal rate of return $($IRR$)$ over $10$ years.

$($b$)$ Determine the discounted payback period $($DPP$).$

$($c$)$ Calculate the accumulated profit at the end of year $10.$