1. a. year 1: \(5000(1.05) = 5250\) ; quarterly: \(5000(1 + \large\frac{.05}{4})^4\)
year 2: \(5000(1.05)^2 =5512.50\); quarterly: \(5000(1 + \large\frac{.05}{4})^8\)
year 3: \(5000(1.05)^3 = 5788.13\); quarterly: \(5000(1 + \large\frac{.05}{4})^{12}\)
year 4: \(5000(1.05)^4 = 6077.53\); quarterly: \(5000(1 + \large\frac{.05}{4})^{16}\)
b. Earnings: \(5000(1 + \large\frac{.05}{n})^{nt}\); where \(n\) is the number of times per year that the interest is calculated and \(t\) is the number of years.
2. Simple interest is \(5000 + 5000(.05)(5) = 6250\)
Compounded daily: \(5000(1 + \large\frac{.05}{360})^{360•5}= 6420.25\)