The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by
where n is the number of times per year the interest is compounded. For continuous compounding, A = Pert. Suppose $10 000 is initially invested at 3.5 percent (r = 0.035).
a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases.
b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
