You are a financial advisor helping a young family create a college fund to provide for their daughter Mary's education. Mary just turned 5. Her parents want to make sure that they can afford to send her wherever her potential allows her to go, starting school on her 18^th birthday. She will only take four years to complete her degree. Currently, tuition and housing costs at top private schools total $35, 000 per year, which are paid at the beginning of each school year. These expenses are expected to increase at the rate of inflation which will run at 4% annually for the next 25 years. In each year through her 18^th birthday, Mary's parents will make a deposit into the college fund so that her college fund will exactly provide for all of the costs of her education when she begins college (the first deposit will be made one year from today). Since her parents expect their income to grow at the rate of 2% annually, they would like the amount that they put each year into the fund to increase in nominal terms at the rate of 2% annually. Mary's parents can earn a nominal rate of 10% annually on their investments and they face a 30% tax rate. a. What do you expect tuition and housing at top private schools to cost during Mary's first year at college? b. In nominal dollars, how much must be in the savings account on Mary's 18^th birthday after the last deposit has been made but before the first tuition and housing payment? c. What should be the amount of the first deposit to the savings account? d. Alternatively, Mary's parents could open a 529 account that allows college savings to grow tax-free. If they saved in this account rather than in a normal investment fund, and still earned the same pre-tax return, how much should be their first deposit