Question 915942: The question is in three parts, but I've solved the second two-thirds. I just don't know HOW to set up a recurrence relation. Assistance would be greatly appreciated.
A person deposits $1000 in an account that yields 9%
interest compounded annually.
a) Set up a recurrence relation for the amount in the account
at the end of n years.
b) Find an explicit formula for the amount in the account
at the end of n years. A = P(1+r/n)^nt where A is the amount of money after n years, r is the annual interest rate (decimal), t is the number of years, P is the principal, n is the number of times the interest is compounded annually (in this case, one).
c) How much money will the account contain after 100
years? A = P(1+r/n)6nt ... A = 1000(1+.09/1)^1*100 ... A = 1000(1.09)^100 ... A = 1090^100 ...
A = 5,529,040.79 of which 1000 is the principal and 5,528,040.79 is the interest.
Answer by ewatrrr(24785)   (Show Source):
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