If a bank pays interest at a rate of i compounded m times a year, then the amount of money Pk at the end of k time periods (where one time period = 1/mth of a year) satisfies the Pk-1 with initial condition P₁ = the initial amount deposited. Find an explicit formula for P recurrence relation Pk = [1 + (-)] The given recurrence relation defines a geometric sequence with constant multiplier ' which is PO + . Therefore, Pn = -[1-(4)- n m for every integer n ≥ 0.

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