Future and present value of an annuity$$ Find the future and present value of a $15-$year ordinary annuity paying $$$$200\mathrm{.}00$ per year at each of the following interest$$ rates:the payment alternative$$either the lump sum or the mixed stream$$that provides the higher future value at the end of $5$ years. Which alternative will she choose?

The future value, $F{V}_n,$ of the lump sum deposit is $$,($Round to the nearest cent.$)$

The future value of the mixed stream of payments is $q.($Round to the nearest cent.$)$

Which alternative will Gina choose? $($Select the best answer below.$)$

Lump sum deposit

Mixed stream of payments

a$.20\%$

b$.10\%$

c$.1\%$

d$.0\mathrm{.}1\%$

e$.$What is the general principle that you see when you compare your answers$$ here? What value are both the present value and future value getting close to as you move from part a to part d$?$