Given the initial information P₀, r and n, Banks will sometimes provide an additional percentage rate called the effective yield. This is understood to be an annual interest rate s% which would yield the same amount at the end of one year under one compounding as the given data under n compoundings.

 (a) If P₀ dollars is invested at an annual rate of 7% compounded quarterly, what is the effective yield?

  (b) If P₀ dollars is invested at an annual rate of 6.75% continuously compounded, what is the effective yield?

(a)The effective annual rate is the equivalent rate for one year:
       So P₀(1+0.07/4)^4t = P₀(1+r)^t  => (1.0175)⁴ = (1+r)=1.071859
          So effective annual rate is 1.07186 - 1 = r => 7.19%

(b) The effective annual rate is the equivalent rate for one year:
       So P₀(e)^rt = P₀(2.718..^0.0675)^t  => (1.06983.) = (1+r)
          So effective annual rate is 1.06983 - 1 = r => 6.98%