Show by algebra that the investment y(t) from a deposit y0 after t years at an interest rate r is y0(t) = y0[1 + r]2 (Interest compounded annually) y0(t) = y0[1 + (r/365)]365t (Interest compounded daily), Recall from calculus that [1 + (1/n)n → e as n →∞; hence [1 + (r/n)nt → ent; thus y0(t) = y0ert (Interest compounded continuously) What ODE does the last function satisfy? Let the initial investment be $s1000 and r = 6%. Compute the value of the investment after 1 year and after 5 years using each of the three formulas. Is there much difference?