Suppose that oil forward prices for $1$ year, $2$ years, and $3$ years are $$74,$ $$69,$ and $$60$ per barrel. The $1-$year effective annual interest rate is $5\mathrm{.}1\%,$ the $2-$year interest rate is $5\mathrm{.}3\%,$ and the $3-$year interest rate is $5\mathrm{.}7\%.$ What is the fixed per$-$barrel price in a $3-$year swap that calls for delivery of $1$ barrel of oil at the end of the first year, $4$ barrels the second year, and $5$ barrels in the third year?

Please solve for correct answer: $$65\mathrm{.}21$