Limiting Cases Math Example 2

Solution

1. 1
   Annual ($n=1$): $A = P(1+r)^t$. Simple compounding once a year.
2. 2
   Monthly ($n=12$): $A = P(1+r/12)^{12t}$. More compounding events per year.
3. 3
   Continuous ($n\to\infty$): $A = Pe^{rt}$ (derived from $\lim_{n\to\infty}(1+r/n)^n = e^r$). Maximum possible growth for rate $r$.
4. 4
   Each case is a limit: moving to more frequent compounding approaches but never exceeds $Pe^{rt}$.