Pamela is also a saver. She sets aside $$100$ per month during her $40$ year career. She invests in the US stock market$*$ through an index fund that averages a $7\%$ annual return over this $40$ year period. a$.$What is the total balance in the account after $40$ years? b$,$ How much of the total did Pamela contribute herself? c$,$ How much money did Pamela make through compounded returns in this investment account? d$,$ Why is Pamela$$s total balance so much greater than Raul$$s even though she contributed the same amount as he did?