Effective Rate of Interest: $eff.i=(1+\frac{i}{ic})^{ic}-1$$j=(1+eff.i)^{\frac{1}{pf}}-1$
Annuity Immediate:
$pv=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*\frac{1-(1+j)^{-n}}{j}$
$fv=pmt*{s_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)^n$
Annuity Due:
$pv=pmt*{\ddot {a}_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)$
$fv=pmt*{\ddot {s}_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)^{n+1}$