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. Irrigated farmland in Phillips County has been selling at $6,000 per acre. If this farmland is expected to increase in value at a compound rate of 3% per year, what will its value be in 20 years. (In this situation the interest rate is interpreted as a growth rate).
2. If the land in question 1 has been increasing at an annual rate of 5%, what was its price 10 years ago?
3. Connie Collateral accepted a $35,000 per year job from 2nd National Bank, but in doing so passed over a job with Community Lenders that started at $32,000 per year. Assuming that the difference in salary persists over the next twenty years, what is the cumulative difference in salary worth today using a 5% assumed rate of increase in salaries?
4. 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.
5. 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).
6. 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)