Question

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?

Answer 1

(a) $A_n = 1.09 \cdot A_{n-1}$

(b) $A_n = 1000 \cdot 1.09^{n}$

(c) $A_{100} = 1000 \cdot 1.09^{100} =$ $5529040.79183$