Eileen is considering buying a $$4000$ computer for her daughter. Eileen hopes that with the computer her daughters schoolwork will improve so much that in two years time she will be offered a full ride scholarship to college. The scholarship is paid for four years and is valued at $$25,000$ per year. Even with the computer the probability that the scholarship will be awarded is $10\%.$ What formula shows the expected NPV for this purchase? a$)-$$$4000+$ $$25,000(1/1^2+$ a$/1\mathrm{.}1^3+1/1\mathrm{.}5^5+1/1\mathrm{.}1^5)$; b$)-$$$4000+(4$ times $$25,000)$; c$)-$$$4000+(4$ times $$2500)$; d$)-$$$4000+$ $$25000(1/1\mathrm{.}1^2+1/1\mathrm{.}1^3+1/1\mathrm{.}1^5+1/1\mathrm{.}2^5)$; e$)4$ times $$2500$