You need $$25,656$ at the end of seven years, and your only investment outlet is a $12$ percent long$-$term certificate of deposit $($compounded annually$).$ With the certificate of deposit, you make an initial investment at the beginning of the first year. Use Appendix B and Appendix C$.($Round $"$PV Factor" to $3$ decimal places. Round the final answers to nearest whole dollar.$)$

a$.$ What single payment could be made at the beginning of the first year to achieve this objective?

Single payment made $

b$.$ What amount could you invest at the end of each year annually for seven years to achieve this same objective?

Amount to be paid $

$2542\mathrm{.}96$