Suppose a company wants to borrow $$10$m for $3$ years, paying interest every year and repaying the $$10$m after $3$ years. The loan is at a variable interest rate, which is set at reference rate r$+1\%.$

The company has an interest rate cap at reference rate r$=6\%.$

How much does the company pay in interest for the loan over all $3$ years if r is $5\%$ in year $1,6\%$ in year $2,$ and $8\%$ in year $3?$ Ignore the cost of the interest rate cap.