Problem
I. Your younger sister, Barbara, will start college in five years. She has just informed your parents that she wants to go to Eastern University, which will cost $50,000 per year for four years (assumed to come at the end of each year). Anticipating Barbara's ambitions, your parents started investing $2,000 per year five years ago and will continue to do so for five more years. Use 12 percent as the appropriate interest rate throughout this problem.
Barbara is now 18 years old (five years have passed), and she wants to get married instead of going to school. Your parents have accumulated the necessary funds for her education.
Instead of her schooling, your parents are paying $30,000 for her upcoming wedding and plan to take a year-end vacation costing $23,000 per year for the next 3 years. (Use a Financial calculator to arrive at the answers.)
i. How much will your parents have at the end of 3 years to help you with graduate school, which you will start then? (Round the final answer to the nearest whole dollar.)
ii. You plan to work on a master's and perhaps a Ph.D. If graduate school costs $37,628 per year, approximately how long will you be able to stay in school based on these funds? (Round the final answer to the nearest whole year.)
II. You are chairperson of the investment fund for Middle Hockey League. You are asked to set up a fund of quarterly payments to be compounded quarterly to accumulate a sum of $510,000 after 10 years at an 12 percent annual rate (40 payments). The first payment into the fund is to occur three months from today, and the last payment is to take place at the end of the tenth year. (Use a Financial calculator to arrive at the answers. Round the final answers to the nearest whole dollar.)
i. Determine how much the quarterly payment should be.
ii. On the day after the sixteenth payment is made (the end of the fourth year) the interest rate goes up to a 16 percent annual rate, and you can earn a 16 percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded quarterly on all funds. Determine how much the revised quarterly payments should be after this rate change (there are 24 payments and compounding dates). The next payment will be in the fourth quarter of the fourth year.