Please solve without the use of excel by discounting the cash flows "by-hand".

1. Find the FV of $10,000 33 years in the future if the opportunity cost rate is 8% (use Excel formulas and basic PV/FV techniques).

2. Find the PV of $1,000,000 to be delivered in 16 years if the opportunity cost rate is 7% (use Excel formulas and basic PV/FV techniques).

3. Would you prefer the following (you can use just formulas for this problem):

1. An ordinary annuity where you receive $500 each year for 20 years if the opportunity cost is 6%
2. An annuity due where you receive $480 each year for 20 years if the opportunity cost rate is 5.9%

4. What is the net present value of the following stream of cash flows assuming the opportunity cost rate is 12%? Solve NPV using each cash flow and the NPV function in Excel (use Excel formulas and basic PV/FV techniques).

Year 0: -$10,000

Year 1: $4,000

Year 2: -$2,000

Year 3: $5,000

Year 4: $3,000

Year 5: $6,000