You are a small business owner who just purchased a machine with expected life of 15 years. You would like to establish a fund to cover the annual maintenance (charges are paid at the end of each service year) of this machine for its lifetime. The maintenance charge is estimated to be $1000 the first year and increases by $100 each year after that. How much should you invest at the beginning of year 1 for this maintenance fund if the interest rate is 5% per annum? (Hint: This problem requires gradient series analysis)