Complete each of the following problems, and be sure to show your work with the appropriate formulation of the basic time value of money formula.
1. Carmelo Anthony may have the chance to sign what has been described as a $100 million dollar contract of 10 equal payments paid annually. Calculate the present value of the contract, assuming a 10% discount rate.
2. An agribusiness manager is saving for a capital purchase of $15,000 that will occur five years from now. If funds can be invested at a 6% interest rate compounded semi-annually, how much must be saved every six months so that the purchase can be made? (A fund used to save for a future purchase is often called a sinking fund).
3. Greg Graduate is planning to purchase a car and repay the loan in 30 equal payments at an annual interest rate of 12%. If the car costs $20,000 and Greg pays a 20% down payment, what is the monthly payment? (Note that this is often called a capital recovery)