Isaiah is in his $50$s and currently does not have a retirement fund. However, he recently read a few articles about the insufficient savings of people in retirement and, as a result, he decides he wants to start now. He saves $$500$ per month for $15$ years and earns an annual return of $7\%$ by investing in the stock market$*$ through an index fund. a$,$ What is the total balance in the account after $15$ years? b$,$ How much of the total did Isaiah contribute himself? c$,$ How much money did Isaiah make through compounded returns in this investment account?