In the previous class you learned how to find the present value of annuity using PMT variable and the PV function. In this class I'd like you to learn how to find an annuity amount. Suppose you need to borrow $300,000 to purchase a house. If mortgage interest rate is 5%, and the term of the loan is 30 years, what is your monthly payment? In order to solve this, you can use a function called PMT in Excel. You can use either PMT function in Google Excel or Microsoft Excel. PMT function looks like this. It has variables such as rate, number of periods, present value and future value. We are going to ignore the least of variable which specifies whether cash flows are at the beginning or at the end of each period. The default is the end of period. Why don't you start Excel and type in =PMT(. The first variable in this function is the interest rate, so type in 5% / 12 as monthly interest rate. The second variable is the number of periods, so, type in 360 or 30 years times 12 months. The third variable is the present value, so type in 300,000, which is the amount you are borrowing. It is important note that in this example, the present value is positive since you are getting the money now. The fourth variable is the future value so type in 0 since you are going to pay off the loan in 30 years and there is nothing to pay back at time 360. The result is -1,610.46. That is your monthly payment is $1,610.46. Next, let's find out how much money you have to pay if you want to pay off the loan at once. Suppose you have borrowed $300,000 at 5% and paid $1,610.46 per month for the past 10 years. That is, the time left until you pay off the loan is 20 years or 240 payments. Suppose you have won on lottery and you'd like to pay up the loan right now. How much money you should pay to pay up the loan today? In order to answer to this questions, you want to use PV function in Excel. Why don't you start Excel? Type in =PV( and you'll see the list of variables. For interest rate, type in 5%/12. For number of periods, type in 20 times 12, or 240. For payment amount, type in 1610.46. For future value, type in 0 since there is nothing left to pay back at the maturity of the loan. Present value of these future payments is 244,025.46. Therefore, what you have to pay today to pay off the loan is $244,025.46. You can apply this method to compute the value of a bond. Bond is a security issued by a company or government that promises to pay interest every period and principal at the maturity. Period interest amount is the same as annuity, so you can discount these cash flows and principal by market interest rate to find the present value of the bond. Let's take a look at an example to learn how to value a bond. Suppose you have a bond that pays interest of $100 every year and $1,000 at the maturity. What is the value of a bond if market interest rate is 5% and maturity is 10 years? You can use PV function to answer to this question. Let's move to Excel and type in =PV(. For interest rate, type in 5%. For number of periods, type in 10. For payment amount, type in 100. For future value type in 1000. You can imagine a cash flow diagram that pays $100 every year for ten years and $1000 in year ten. The present value is -1,386.09. That is, the value of a bond is $1,386.09.