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What is the recurrence relation that for the following statement (in description)

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$500 is deposited into an account that pays 5% interest at the beginning of the next year. At the end of every year, besides the firs, as additional $100 is deposited into the account


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If we were to take that literally, the $100 is deposited at the end of the year. A tick of the clock later it is the beginning of the new year. At that time, 5% interest is paid on the entire amount, which would include that $100 that was just deposited. That is no way to run a business. Also, the interest is paid, but it does not say whether it is paid into the account or paid out directly to the account holder.


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