Suppose that Kelly and Zack just had their first baby today and they wish to ensure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7% (compounded annually). The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Assuming that the parents make the 18th deposit for their daughter's 18th birthday. Then how much will they have for their daughters college expenses on her 18th birthday? Note that there are four (4) parts to this question (a, b, c, d) a. Assuming $2000 on first birthday, growing by 5% per year (compounded annually), how much will they have on her 18th birthday? b. Suppose that they wish to have saved $160,000 saved by their daughter's 18th birthday, and assume that they continue to earn 7% compounded annually on their savings, by what growth rate must they grow their annual contributions to have $160,000 saved by her 18th birthday? c. Suppose, now, that they wish to have saved $160,000 saved by their daughter's 18th birthday, and assume that they continue to earn 7% compounded annually on their savings, but that they wish to save the same amount at the end of each year, instead of increasing the amount of savings. How much must they save each year in order to have $160,000 saved by her 18th birthday? d. Suppose, instead, that the couple decides to deposit their savings into an account that earns 7% APR but that the rate of return is compounded quarterly, instead of annually. Suppose, now, that the couple will make the first deposit when their daughter is three months old (three months from now) and that they plan to increase the size of the deposit 5% each quarter. (On the daughter's 18th birthday, they will have made 72 deposits.) How much will have they saved by the daughter's 18th birthday?

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