c$)$ An investment is expected to produce the following annual year$-$end cash flows:

year $1$: $$5,000$ year $4$: $$5,000$

year $2$: $$1,000$ year $5$: $$6,000$

year $3$: $$0,$ year $6$: $$863\mathrm{.}65$

The investment will cost $$13,000$ today.

i$)$ Will this investment be profitable?

ii$)$ What will be the IRR $($compounded annually$)$ on this investment?

iii$)$ Prove your answer in $(b)$ by showing how much of each year's cash flow is recovery of the $$13,000$ investment and how much of the cash flow is return on investment.