The Murphy family, is setting up a retirement plan. They will make fixed monthly contributions to a pension fund, until Mr and Mrs Murphy retire, that is, 35 years from now. After retirement, the family are planning to withdraw a fixed amount C each month for the next 25 years. Assume a fixed 7.8% annual discount rate.

a) If the Murphys plan to withdraw $3,000 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 $200 each month to the fund now?

Please include the work too !