Answer to Question #136791 in Discrete Mathematics for Promise Omiponle

Question #136791
1) A person deposits 1000 USD into an account that yields 9 percent interest compounded annually. Let An denote the amount of money in the account after n years.
(a) Set up a recurrence relation for An.
(b) Find an explicit formula for An.
(c) How much money will be in the account after 100 years?
1
Expert's answer
2020-10-13T14:45:53-0400

(a) An=1.09An1A_n = 1.09 \cdot A_{n-1}

(b) An=10001.09nA_n = 1000 \cdot 1.09^{n}

(c) A100=10001.09100=A_{100} = 1000 \cdot 1.09^{100} = 5529040.791835529040.79183


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