2. (25p) Suppose you take a loan of $25,000 from a bank at the beginning of each year for four years during your college education to pay for the college expenses (in total $100,000). You graduate at the end of 4th year. The loan's interest is 12% per year, compounded monthly. To pay off completely the loan, the bank expects you to make 60 uniform monthly payments starting six months after the graduation. The bank is exible with this payment plan in the sense that there is no penalty if you prefer to pay off the loan earlier at any time by making extra payments. a) Draw a cash ow diagram that illustrates this loan problem. Use the notation A for the monthly payments you are expected to make to the bank. Consider the start date of college as time 0. b) Compute the uniform monthly payment, A. 1:) Of the 25\":L monthly payment, what is the interest and the principal paid? (1) Suppose that after making 10 payments, you decide that you can afford paying the loan earlier by making an extra payment of size $15,000 and increasing the monthly payment size to $4,000. Compute the number of remaining payments with this new payment plan. Use the 1% interest table and the linear interpolation