We construct exponentially fitted interpolation formulas using the values of the ${omega}$-dependent function $f$ as well as its derivatives up to the $n$th order at a finite number of nodes on a closed interval ${Omega}$. The function $f$ is of the form, $$f(x)=f_1(x)cos({omega}x)+f_2(x)sin({omega}x),x{in}{Omega}$$, where $f_1$ and $f_2$ are smooth enough to be approximated by polynomials on ${Omega}$. Some properties of the formulas are newly found. The properties are numerically investigated and reexamined by producing some figures.