Julian and Jonathan are twin brothers $($and so were born on the same day$).$ Today, both turned $25.$ Their grandfather began putting $$3,450$ per year into a trust fund for Julian on his $20$th birthday, and he just made a $6$th payment into the fund. The grandfather $($or his estate's trustee$)$ will make $40$ more $$3,450$ payments until a $46$th and final payment is made on Julian's $65$th birthday. The grandfather set things up this way because he wants Julian to work, not be a "trust fund baby," but he also wants to ensure that Julian is provided for in his old age.

Until now, the grandfather has been disappointed with Jonathan and so has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee to make $40$ additional equal annual payments until Jonathan turns $65,$ when the $41$st and final payment will be made. If both trusts earn an annual return of $8\%,$ how much must the grandfather put into Jonathan's trust today and each subsequent year to enable him to have the same retirement nest egg as Julian after the last payment is made on their $65$th birthday? $($SOLVE USING A FINANCIAL CALCULATOR PLEASE$)$

Select the correct answer.

a$.$ $$5,141$

b$.$ $$5,117$

c$.$ $$5,129$

d$.$ $$5,093$

e$.$ $$5,105$