e

Definition of e:

e  =  lim     (1 + 1/n)ⁿ
        n->oo

Compound Interest Formula:

A  =  A₀(1 + r/n)^nt

where A = amount at end of t years
        A₀ = initial amount
           r = annual interest rate
           n = number of compounding periods in one year
            t = number of years

Continuous Interest Formula:

• A  =  A₀(1 + r/n)^nt
• Let m = n/r
  Then mr = n
• And  A  =  A₀(1 + r/(mr))^mrt
  or     A  =  A₀(1 + 1/m)^mrt
  or    A  =  A₀^[(1 + 1/m)^m]^rt
• As m ->oo we can apply the definition of e and write
• A  =  A₀e^rt

Problems