Time value$$Annuities Personal Finance Problem Marian Kirk wishes to select the better of two $8-$year annuities. Annuity $1$ is an ordinary annuity of $$2,180$ per year for $8$ years. Annuity $2$ is an annuity due of $$2,090$ per year for $8$ years.

a$.$ Find the future value of both annuities at the end of year $8,$ assuming that Marian can earn $(1)3\%$ annual interest and $(2)6\%$ 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 $(1)3\%$ and $(2)6\%$ interest rates..

c$.$ Find the present value of both annuities, assuming that Marian can earn $(1)3\%$ annual interest and $(2)6\%$ annual interest.

d$.$ Use your findings in part c to indicate which annuity has the greater present value for both the $(1)3\%$ and $(2)6\%$ interest rates.

e$.$ Briefly compare, contrast, and explain any differences between your findings using the $3\%$ and $6\%$ interest rates in parts $b$ and $d.$

a$.$ The future value of Annuity $1$ at $3\%$ interest is $ $($Round to the nearest cent.$)$