PART 1
a. To raise $290000 in 20 periods of 6 months at 4.125% semiannually would need a principal investment of P:
290000=P(1.04125)^20=2.2444P approx. P=290000/2.2444=$129210.47 approx.
b. The surcharge would be 129210.47/958=$134.88 per homeowner.
PART 2
a. Assuming $783000 is needed in total for the water towers (rather than this amount each), 15 years is 180 months at 9/12=0.75% per month. The principal amount, P, is given by 783000=P1.0075^180=3.838P. The number 3.838 is the growth rate of the investment over 15 years. So P=$204010.21 approx.
b. We deduct $50000 from 783000 to give $733000 as the effective cost of the towers to the homeowners. So P=733000/3.838=$190982.73 to be divided between 2682 homeowners=$71.21 surcharge.