You can invest funds at $6\mathrm{.}4\%($APR$).$ You are considering buying an annuity and are comparing two alternatives. Both of these are $14$ years in length, with the same number of monthly payments $($to you$)$ of $$5072.$ The first instrument pays at the "end" of the month while the second pays at the "beginning" of the month. You believe that the second alternative must be worth more as the money comes to you faster, but how much more is it worth to you?

a$.3348$

b$.2997$

C$.4109$

d$.2458$

e$.2795$