Your life is changing rapidly. You have graduated from the prestigious School of Business, and are enjoying the fruits of your hard-earned education. But there are big changes on the horizon (well, big changes that come in small packages): You (or your significant other) are (is) pregnant and the baby is due around the first week of July 2023. Of course your little pride-and-joy is going to be cute AND smart.

After much consultation, your significant other and you have decided that you want to send the little one to a private college (when the time comes). Private colleges are very expensive. The average cost is estimated to be around $36,993 for one year (July 2022). This cost covers tuition, fees, room, and board and is based on a private, four-year school in the United States. You expect these costs to increase by 2% per year over the current annual rate of inflation of 1.9%, i.e., 3.9% annual cost increases over the foreseeable future. Your child will most likely begin school eighteen (18) years after birth. Schools tend to demand payments upfront. Assume the cost of the whole first year tuition is due in July 2041. The whole second year tuition is due in July 2042, etc. You expect to invest your money in a manner that returns 7.50% per year over the foreseeable future. You want to start saving soon. In fact, you plan to invest money every year. To be precise, you will put away money once a year, every July, starting when the baby is born, and ending in July, 2040.

A. (10 points) Suppose you want to save the same (constant) amount each year in nominal dollars. How much will you have to save each year so that there is enough money to send your child to college?

B. (10 points) In the first part of this problem, you calculated the constant nominal amount saved each year. Of course, in real terms, the value of these amounts gets less and less over time due to inflation. Suppose instead that you want to save the same (constant) amount each year in real dollars. How much will you have to save each year so that there is enough money to send your child to college? In addition, provide the corresponding (increasing) cash flows saved in nominal dollars made each year.

C. (5 points) Are your answers to parts A and B above consistent in present value terms (are they equal)? If yes, why? If not, why not?