Suppose your family and friends know you are taking the class in which you learned about time value of money. Four of them came separately to ask questions relating to time value of money. Use the applicable interest table at the end of the book to compute the unknowns for your four relatives. Note that each is independent.

a. Your friend asked how much he must contribute at the end of the each of the next eight years if he wants to accumulate $90,000 in his account by the end of the eighth year. Cousin told you the interest is compounded annually and the account will earn interest rate of 8%.

b. Your 40-year old Aunt plans to retire at age 65. She is getting a late start but wants to start contributing towards her retirement from now (age 40) through age 64. How much must she contribute each year if he plans to accumulate $500,000 by the time he retires; if he will earn 12% annual interest and interest is compounded annually?

c. Your sister owes $47,347 on her student loan. She wants to pay off before she retires. She has $20,000 today and she will invest the $20,000 in an account that pays 9% interest. How many years will it take for the $20,000 to grow so she can have enough money to pay off the $47,347 debt assume the debt amount is fixed?

d. Your uncle currently has a $27,600 loan. He plans to repay the loan in four years. She plans to invest $19,553 for the next four years and use the principal and interest balance in the account to pay off the loan. What rate of interest must your uncle earn annually so he can have enough to pay off the loan?