Discrete math A bank account pats interest at the rate of 100% a year. Assume an

Question

Discrete math

A bank account pats interest at the rate of 100% a year. Assume an initial balance of P, which accumulates to s_n after n years Now we have to find a recursive definition for s_n Recursion refers to expressing a term of the sequence of the preceding term. Let us assume s_0 = P is the initial amount For n > 0, Since the rate at which principle amounts per annum is given by 100% and n gives the number of yers. Hence; s_1 = p + ip = (1 + i)p s_2 = (1 + i)p + i(1 + i)p = (1 + i)s_1 and so on. s_n = (1 + i)s_n - 1. Therefore we have the recurrence relation s_n = (1 + i)s_n - 1

Explanation / Answer

total amount after one year = principal amount P + interest for one year

interest = PTR/100= PX1X100i/100= iP (since interest rate = 100i ,time T=1 year)

total amount after one year= P + iP

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