Hi, everybody. In this class I'd like to review the concept of time value of money using various real-world examples. First let's look at a case that American Indians sold all of Manhattan Island to Peter Minuit for about $24 in goods and trinkets. This is quite often used example to show the effect of compounding. If the Indians had invested the $24 at 10% until year 2016, that is for 390 years, the future value of $24 is is $333.7 quadrillion. If you had this money, you could buy the United States. You can compute the future value of $24 invested at 10% rate for 390 years using Excel. First type in =FV. Type in 10% percent for rate. Type in 390 for NPER. Type in 0 for PMT. Type in -24 for present value. And then the result is $333.7 quadrillion. However, it is unlikely that Indians found an investment opportunity with 10% return for 390 years. Next, suppose you are given a savings certificate that will pay you $100 in 25 years. If the going interest rate is 10% per year, what is the actual value of the certificate? In order to find the actual value, you need to find the present value of $100 in 25 years discounted at 10%. Why don't you enter =PV? Why don't you type in 10% for rate? Type in 25 or NPER. Type in 0 for PMT. Type in -100 for future value. And the result is 9.23. Therefore, the actual value of the certificate is not $100, but $9.23. Next, suppose you'd like to retire in 30 years as a millionaire. If you have $100,000 today, what rate of return do you need to earn to achieve your goal? In this question you know that you are looking for rate. So type in =RATE. Type in 30 for NPER. Type in 0 for PMT. Type in -100,000 for present value. Type in 1 million for future value. The result is 7.98%. Therefore the rate of return you need to earn to achieve your goal is 7.98% per year. Next suppose you can afford to pay $300 per month towards a new sports car. You call up your local bank and find out that the going rate is 6% per year and loan period is 60 months, how much can you borrow? To determine how much you can borrow you need to calculate the present value of $300 per month for 60 months at 0.5% per month. Type in =PV. Type in 6% over 12 for rate. Type in 60 for NPER. Type in -300 for PMT. Type in 0 for future value. The result is $15,517.67. Therefore $15,517 is what you can afford to borrow and repay. Next, suppose you are borrowing a 5-year loan with a 20-year amortization. This means that you are making a payment every month of a fixed amount based on a 20-year amortization. But after 60 months you make a single payment called a “balloon” or “bullet” to pay off the loan. Suppose your loan amount is $1 million with a 6% APR. You need to use PMT function. The monthly payment will be equal payment. Type in 6%/12 for rate. Type in 240 for NPER. Type in 1 million for present value. Type in 0 for future value. And the result is $7,164.31. The balloon payment will be then, type in =PV(6%/12 for rate. Type in 12*15 for NPER. Type in -7,164.31 for PMT and 0 for future value. And the result is $848,995.92.