Problem 6.1. (5 points) Roger’s aunt Agatha decided to set up a monthly supplemental income for her favourite nephew (Roger, of course). Roger is supposed to get 1,000 at the end of each month for the first year. Then, for the second year his monthly allowances increase to 1,200. The same increase happens each year for as long as Roger receives this allowance. So, the amount he gets at the end of every month during year j is equal to

1,000+ 2000 - 1) = 800 + 2007

Roger is supposed to be receiving the payments for 20 years. To make this possible aunt Agatha opened an account with the annual effective interest rate equal to 0.05. She made one initial deposit A which was just sufficient to finance Roger's al- lowance. Find A.