As a risk$-$neutral lender, you know that there are two types of borrowers:

Type X: Earns $$200$ with $80\%$ chance, needs $$100$ to start

Type Y: Earns $$150$ with $95\%$ chance. needs $$100$ to start

If you can tell who is Type $x$ and who is Type $Y,$ what is the minimum interest you would charge for Type $Y?$

Please provide your answer in percentage value and display two digits after the decimal in your answers.