Suppose that an initial bank deposit was $2.000 At the end of each year it is increased by 5% and...
Suppose that an initial bank deposit was $2.000 At the end of each year it is increased by 5% and an additional $500 is deposited amount of the deposit after the nth year. Write the recurrence relation with initial condition for the amount deposited after nth year. Next provide the solution.
Homework Answers
Please find the solution with explanation: Initial condition P0 = 2000(initial deposit) At the end of first year P1 = principal + interest on principal + additional deposit P1 = 2000 + ((5/100)* 2000) + 500 = 2000 + 100 + 500 = 2600 At the end of second year P2 = previous principal(P1) + interest on previous principal(P1) + additional deposit P1 = 2600 + ((5/100)* 2600) + 500 = 2600 + 130 + 500 = 3230 ... ... ... Pn = previous principal(Pn-1) + interest on previous principal + additional deposit Pn = Pn-1 + ((5/100)* Pn-1) + 500 = Pn-1 + 0.05Pn-1 + 500 = 1.05Pn-1 + 500 Solution: P0 = 2000 (initial condition) Pn = 1.05Pn-1 + 500 (Recurrance relation)
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