Answer
$ r=10\%$
Work Step by Step
The interest on the loan (without the fee) is
$INT=PV(rt)=5000\times 0.09\times 2=\$ 900$
With the additional fee of $\$ 100,$ it becomes $\$ 1000.$
With this new interest, we find r from
$INT_{new}=PV(rt)$
$1000=5000(r\cdot 2)$
$1000=10,000r\quad/\div 10,000$
$r=0.1$
$ r=10\%$
