ou were recently admitted to college, and your Aunt Tillie has agreed to fund the tuition for your education. The admissions representative at your college says that tuition might rise approximately 5 percent per year. Aunt Tillie has agreed to deposit a lump sum today that will cover your tuition for four years, but she needs to know the amount of the initial deposit. Your aunt is no longer able to take care of herself, so she also wants to set aside a lump sum of money to pay her rent in an assisted-living facility for the next three years. The facility has agreed not to raise her rent, if she signs a three year lease upfront.

It's now four years later, and thanks to your aunt's generosity, you have graduated from college. She has offered to lend you the money to buy your first, new car. You are interested in calculating the payment amount on a $35,000 car loan at 6 percent for five years. She has also agreed to accept five annual payments instead of monthly payments.

It seems there's no end to Aunt Tillie's generosity. She has now agreed to loan you $10,000 for the down payment on a home. You have decided to structure the loan, so that the payment amount remains constant through the term of the contract and you can budget for a consistent loan payment each month.

Which of the following calculations will you perform to determine the amount of the initial deposit necessary to fund your college education?