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An interest rate is the rate at which interest is paid by a borrower (debtor) for the use of money that they borrow from a lender (creditor).

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Is the $NPV$ always a decreasing function in $r$

I was able to prove that, for positive Cash Flows $f_i$ and any value of $f_0$, the $NPV$ function is decreasing in $r$, hence, for $r_m<r_p=IRR$, then $NPV(r_m)>NPV(r_p)=0$. $$ NPV(r,f_i)=\sum_{i=0}^ …