You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% EAR, compounded monthly. Two years into your college, that is, after having made the first 24 payments and with 24 payments remaining, you win a lottery of $10,000 and you will use the lottery winnings to make a lump sum payment of $10,000 toward reducing your outstanding loan balance: a. What are your new reduced monthly payments if you still intend to make all the 24 remaining monthly payments toward your loan? b. After making the $10,000 repayment say, you and your bank decide that you will repay the loan over the coming 10 months and not 24 remaining months, what are your new monthly payments for the next 10 months? C. Suppose instead, that you used $7000 from your lottery winnings to buy a car and used only the remaining $3000 to make one lump-sum payment toward the loan. You also continued to make original $500 payments every month, how many more months will it take for you to repay the entire remaining balance, if your monthly payments continue to be $500 (round the answer it to the nearest whole number)