Suppose you borrow $20,000 at an effective periodic rate of i. The loan will be paid back with 20 payments at the end of each period. Each payment will consist of $1,000 plus the interest owed for that period. For example, the first payment will be $1, 000 + $20, 000i. Show that the present value of these payments at interest rate i is $20,000. Hint: Try to figure out what the pattern the payments follow. Follow up hint: You may recognize one of the pieces as a decreasing annuity.

Please solve by hand showing work.