Many savings banks now advertise continuous compounding of interest. This means that the amount of money P(t) on deposit at time t, satisfies the differential equation dP(r)/dt = rP(t) where r is the annual interest rate and r is measured in years. Let Po denote the original principal. (a) Show that P (I)= Poer. (b) Let r = 0.0575, 0.065, 0.0675, and 0.075. Show that er= 1.05919, 1.06716, 1.06983, and 1.07788, respectively. Thus, the effective annual yield on interest rates of 5$, 6f, 65, and 7t% should be 5.919, 6.716, 6.983, and 7.788% respectively. Most banks, however, advertise effective annual yields of 6, 6.81, 7.08, and 7.9%, respectively. The reason for this discrepancy is that banks calculate a daily rate of interest based on 360 days, and they pay interest for each day money is on deposit. For a year, one gets five extra days. Thus, we must multiply the annual yields of 5.919, 6.716, 6.983, and7.788% by 365/360, and then we obtain the advertised values.(c) It is interesting to note that the Old Colony Cooperative Bank in Rhode Islandadvertises an effective annual yield of 6.72% on an annual interest rateof 6f% (the lower value), and an effective annual yield of 7.9% on an annualinterest rate of 7;%. Thus they are inconsistent.

PROJECT: mulching trees, debris removal Project Confirmation Each participant should bring: Thank you for volunteering to help with the Deboer Park • Liability waiver Project! Details for the day are as follows: • Work gloves Daate:Occtober...