Compound interest
Recurrence relations can be used to model a wide variety of problems,
At the annual interest rate of 10%, and with the initial balance of
b0 dollars, what would be the balance on the account after n years?
The following recurrence relation expresses the balance after n years
in terms of the balance after n-1 years:
b2= 1.1b1 = 1.1?1.1b0 = (1.1)2b0
b3= 1.1b2 = 1.1?(1.1)2b0 = (1.1)3b0
bn= 1.1bn-1 = 1.1?(1.1)n-1b0 = (1.1)nb0
By mathematical induction,
recurrence relation defines
b10=2.6b0, b30=17.5b0,...