A client is concerned about the impact that inflation will have on her retirement income. The client currently earns $$40,000$ per year. Assuming that inflation averages $2\mathrm{.}25\%$ for the first five years, $2\mathrm{.}5\%$ for the next five years and $3\mathrm{.}25\%$ for the remaining time until retirement.What amount must her first$-$year retirement income be when she retires $13$ years from now if she wants it to equal the purchasing power of her current earnings?

Group of answer choices

$$54,998$

$$53,800$

$$52,892$

$$55,675$