a. Carl would like to support the university education of his grandson, John, who will start his university exactly two years from today. John will be at the university for three years, and he has to pay his tuition at the beginning of each year. The tuition each year will be $5,000. How much Carl needs to invest today to ensure that he can make the three payments for his grandson? Assume that Carl can earn a 7% return per year on his investment (compounded annually). (5 marks) b. Now suppose that Carl's plan has changed. Carl will take a loan of $5,000 at the beginning of each year from the bank to pay for the three years of John's university education. Carl will take the loan at an annual interest rate of 10%, and the interest is compounded annually. Carl will start paying off the loan 3 years after receiving the last portion of the loan (i.e., her first payment will occur at t=7 ). He will pay off the loan in 4 yearly installments of equal amount. How much each installment will be