Assume that your child has just turned 5 years old and you are starting to prepare for her college education. You assume that she will start college on her 18^(th ) birthday (in 13 years). that she will graduate on her 22^(nd ) birthday (in 17 years), and that tultion costs for her four years of college (to be paid on her 18^(th ),19^(th ),20^(th ), and 21^(st ) birthdays) will be as listed in the table below. You would like to make monthly deposits into an account over the next 17 years, where the first deposit occurs today (her 5^(th ) birthday) and the last deposit will be made one month before her 22^(nd ) birthday (this is a total of 204 payments). You wish to accomplish two things: (1) to be able to pay her tuition each year, and (2) to be able to give her $25,000 in cash on her 22^(nd ) birthday as a graduation present. Assume that your deposits can earn an annual nominal rate of return of 9 percent, but where interest is compounded monthly. Given this information, determine the amount of the monthly deposit that will be needed to meet your goals.
\table[[Year,Tution],[18,$18,000