The Goodhart family, whose acquaintance we have made earlier, are setting up a retirement plan. They will make fixed monthly contributions to a pension fund, until Mr and Mrs Goodhart retire $30$ years from now. After retirement, the family are planning to withdraw a fixed amount A each month for the next $20$ years. Assume that the fund earns a fixed $6\%$ return.a$)$ If the Goodharts plan to withdraw $2,000$ each month, how much would they have to pay into the fund each month before they retire?b$)$ How much can the family withdraw each month after retirement, if they can only afford to contribute $250$ each month to the fund now?