Officers of the Night Watch are raising money to provide the family of fallen Sgt. John Keel with a monthly allowance for the next 25 years: $50 in each December, and $30 per month in all other months. Suppose that the nominal annual interest rate is 3% compounded monthly, and the first payment is made on June 1.
(a) How much money do the officers have to raise by the time of the first payment?
(b) If the calendar of Ankh-Morpork has 13 months, and June is the 7th month of the year, how much money do the officers have to raise by the time of the first payment?