How much more is a perpetuity paying $$5000$ at the end of year worth than an annuity paying the same annual amounts at the end of each year for $30$ years? Assume an interest rate of $5\%.$

a$.$

$$21,976\mathrm{.}29$

b$.$

$$23,137\mathrm{.}74$

c$.$

$$10,635\mathrm{.}08$

d$.$

$$50,000\mathrm{.}00$