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Question

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. c) How much money will the account contain after 100 years?

Solution

VerifiedStep 1

1 of 4Given:

$a_0=1000$

$r=9\%=0.09$

(a) Let $a_n$ represents the amount in the account at the end of $n$ years.

Each year 9% interest is added to the account. Thus the amount in the account is the amount of the previous year increased by 9% of the amount of the previous year.

$a_n=a_{n-1}+9\%\cdot a_{n-1}=a_{n-1}+0.09\cdot a_{n-1}=1.09\cdot a_{n-1}$

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