Your child will go to college $12$ years from now and will require $$20,000,$ $$21,000,$ $$22,000,$ and $$23,000$ at the beginning of each year in school. In addition, you and your spouse plan to retire in $20$ years. You want to have $$75,000$ available for each of your expected $15$ years of retirement. These funds will need to be available at the beginning of each year. You currently have $$15,000$ that can be invested to meet these objectives. Assuming you can earn a $4$ percent rate of interest over the entire time period and ignoring taxes, how much must you invest at the end of each month over the next $20$ years in order to meet your financial objectives?

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A perpetuity is defined as an infinite stream of equal, consecutive cash payments. This being so$,$ explain how it is possible to place a finite present value on a perpetuity assuming the use of a positive discount rate.