a. Problem 1: (15 points) You are saving for a graduation trip the summer after graduation. You just completed your freshman year, and you expect to graduate at the end of 4 years. Therefore, you have 3 years to save for the trip. You want to save $13,000 for the trip. You have a savings account that earns 10% compounded monthly. Consider each of the 4 scenarios below as separate scenarios and answer each question independent of the others. Assume you make a single lump sum investment in the account today and do not touch it for the remaining 3 years. How much do you need to invest as a lump sum to have enough for your trip in 3 years? b. Assume you make uniform payments each month. How much must you put in the account each month for 3 years to have enough for the trip in 3 years? C. Assume you have already saved $3,800 and it is in the account now. You plan to add $200 a month for 3 years. How much will you have the end of 3 years? How much will you need in graduation gifts to make up the difference in the cost of the trip? d. Assume you can only contribute $100 each month to the savings account. How much do you need to invest as a single lump sum today so that you have enough for your trip in 3 years