Which is the lump$-$sum amount needed to generate a retirement income of $$45000$ per year for $15$ years, assuming interest at $7\%$ per year, compounded annually?

a$)$ $$357420\mathrm{.}88$

b$)$ $$644514\mathrm{.}51$

c$)$ $$450452\mathrm{.}65$

d$)$ $$409856\mathrm{.}13$