Time value$-$Annuities Personal Finance Problem Marian Kirk wishes to select the better of two $8-$year annuities. Annuity $1$ is an ordinary annuity of $$2,770$ per year for $8$ years.

Annuity $2$ is an annuity due of $$2,610$ per year for $8$ years.

a$.$ Find the future value of both annuities at the end of year $8,$ assuming that Marian can earn $(1)6\%$ annual interest and $(2)12\%$ annual interest.

b$.$ Use your findings in part a to indicate which annuity has the greater future value at the end of year $8$ for both the $(1)6\%$ and $(2)12\%$ interest rates..

c$.$ Find the present value of both annuities, assuming that Marian can earn $(1)6\%$ annual interest and $(2)12\%$ annual interest.

d$.$ Use your findings in part $c$ to indicate which annuity has the greater present value for both the $(1)6\%$ and $(2)12\%$ interest rates.

e$.$ Briefly compare, contrast, and explain any differences between your findings using the $6\%$ and $12\%$ interest rates in parts b and d$.$

a$.$ The future value of Annuity $1$ at $6\%$ interest is $

$($Round to the nearest cent.$)$