How to calculate the future value of some cash.


  • : periods per year
  • : duration (in years)
  • : number of compounding periods.
  • : Present value = Principal = Amount lent/borrowed at time
    • : Future Value = Amount at time
  • : annual interest
  • : Interest Rate


  • Banker’s Rule is a common way to simplify math calculations.
  • .

def. Simple Interest ⇒ Only principal is invested at the end of each year

def. Compound Interest Divide into periods per year, and compound for periods:

Divide into periods per year, and compound for years (equivalent formula):

⇒ Conceptual Demonstration of Compounding Interest:

def. Continuous Compounding Compound for years (equivalent formula):

⇒ You can get this formula from compound interest and setting

def. Fractional Compounding

⇒ You can do things like ” of daily compounding.”


For a fixed , is monotonic for . ⇒ Proof in slides. (Using binomial expansion)