Determine the difference between the present value of a $$51,000$ twenty$-$year annuity earning $6\%$ interest compounded annually versus a $$51,000$ twenty$-$year growing annuity earning $6\%$ interest compounded annually and having a $3\%$ annuity growth rate.

a$.$

$$177,672\mathrm{.}18$

b$.$

$$147,672\mathrm{.}18$

c$.$

$$157,672\mathrm{.}18$

d$.$

$$137,672\mathrm{.}18$

e$.$

$$167,672\mathrm{.}18$