$$250,000$ will be needed by the Body Corporate in $15$ years time to replace the lift in an apartment block. It is expected that a fixed compound rate of $5\%$ can be arranged. How much should the Body Corporate invest each year to ensure that sufficient funds will be available at the required time?

a$)$ $$11,585\mathrm{.}57$

b$)$ $$37,078\mathrm{.}88$

c$)$ $$6,176\mathrm{.}62$

d$)$ $$15,833\mathrm{.}33$

Please show working and explain the process. Thank you.