Raul is a saver. He sets aside $$100$ per month during his career of $40$ years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns $1\mathrm{.}5\%$ interest per year. Total balance in the account after $40$ years: $$65,715,$ and the total Raul did contribute: $$48,000,$ Raul make through compound returns in this investment account: $$17,715.$

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?