5-1 Time Lines What does Year 0 represent in a cash flow timeline? 5-2 Future Values Calculate the future value given the following information below: Amount invested at year 0: Number of years invested Interested rate with annual compounding: $80 4 3% 5-3 Present Values-Question1 Calculate the present value given the following information below: Amount at end of year 6 $1,000 3% Interested rate with annual compounding: 5-3 Present Values -Question 2 As a follow up to the last question, if we're in agreement that the correct interest rate is 3%, which do you prefer: (1) $1,000 at the end of year 6 or (2) the PV you found in the last part? 5-4 and 5.5 Finding I and N An investor wants to invest a lump sum of $1,000 and have $2,000 at the end of ten years. Assuming annual compounding, what interest rate is required to reach this goal? 5-6 Annuities An annuity is a stream of_ _payments either at the or the of a period. This is like paying rent at the beginning of each month for 12 months or paying a mortgage payment at the end of each month for 12 months. An annuity is a stream of pavments either at the or the _of a period. 5-7 Future Value of an Ordinary Annuity Calculate the future value of an ordinary annuity given the following information N: 1(annual): 7% Payments of S100 made at the end of each period 5-8 Future Value of an Annuity Due Calculate the future value of an annuity due given the following information Number of periods Interest rate Payments of S100 made at the beginning of each period 4 9% 5-9 Present Value of an Ordinary Annuity Calculate the present value of an ordinary annuity given the following information Number of periods Interest rate Future value Payments 3% $0 $500 5-10 Finding PMT, N, and I A worker wants to have $1,000,000 by the time he retires. The worker puts $10,000 into a savings account at the end of every year that earns 5% compounded annually. How many years of working will it take until the worker can retire? 5-10a Finding Annuity Payment, PMT A worker wants to have $2,000,000 by the time they retire. The worker plans on working 40 years until he retires. What yearly payment must be put into a savings account at the end of each year if the savings account yields 8% annually? 5-10c Finding the Interest Rate, I A student beginning their career has $10,000 in savings. They plan to retire in 45 years while investing $6,000 every year at the end of the year compounded annually in the hopes of having $1,000,000 at retirement. What is the required rate of interest to achieve this goal? 5-11 Perpetuities A lottery winner wins a $50,000/year prize ends upon the death of the winner. However, the lottery winner, who is a scientist, discovers a drug that makes him immortal, meaning the payments will continue to perpetuity. What is the present value of the lottery prize if the discount rate is 10%? 5-12 Uneven Cash Flows Calculate the net present value of the following cash flows with an annual interest rate of 2%. Year 0: Year 1: Year 2: Year 3: Year 4: -300 +200 +200 +700 -100 5-13 Future Value of an Uneven Cash Flow Stream Calculate the future value of the following cash flows with an annual interest rate of 3%. Year 0: Year 1 Year 2: Year 3: Year 4: 300 50 100 500 Extra Video: Continuous Compounding How many times per year is a principal compounded in one year with continuous compounding