Now we are ready to make a formula for present value. PV is Present Value. As we learned in the previous class, present value is future value divided by (1 + Interest rate). Let's take a look at a few examples to understand how to find present value given future value and interest rate. Suppose we need $650 to buy an iPhone next year. You can earn 3% on your money. How much do you have to put up today? In this example, future value is $650. Rate is 3%. The equation is $650 divided by (1+3%) is equal to $631.07. Thus, you have to put up $631.07 today to buy an iPhone next year. You can solve this with Excel. Let's find PV using Excel template. First, type in 650 for FV Since that is the amount you need in the future. Type in 3% for rate. Since it is the interest rate. Type in 0 for PMT. And type in 1 for NPER Since you want to buy an iPhone in 1 year. Then you'll see that PV is 631.07 As you've learned already Negative PV means cash outflow or investment. That is, you have to put up $631.07 at 3% interest rate to earn $650 in one year. We can make sure whether your answer is correct by calculating FV using PV you found from Excel. Let's move to Excel again and type in 631.07 for PV. Type in 3% for rate. Type in zero for PMT Type in 1 for NPER And you'll get FV of $650. That is exactly what you need. Let's take a look at another example. You are interested in purchasing a car that costs $70,000 in three years. If you can earn 6% on your money. How much do you have to invest today to buy the car in three years? In this example, future value is $70,000. Rate is 6%, and the number of periods is 3 years. The equation is $70,000 divided by one plus 6% raised to the power of three is equal to $58,773. Thus, you have to invest $58,773 today to buy the car in three years. We can solve this with Excel. Let's start the Excel and type in numbers. Type in 70,000 for FV. Type in 6% for rate. Type in 0 for PMT. Type in 3 for NPER. And you'll get PV of $58,773.35. This is same as what you get with the mathematical formula. We can make sure whether your answer is correct by calculating FV using PV you found from Excel. Let's move to Excel. And type in $58,773 for PV Type in 6% for rate Type in zero for PMT Type in 3 for NPER And you'll get FV of $69,999.58, which is about $70,000. And the difference is due to the rounding error in the calculation of PV. Let's take a look at another example. Assume an annual interest rate is 7%. How much would an investor need to lend today so that she could receive $800 in two years? In this example future value is 800. Rate is 7% and the number periods is 2 years. The equation is $800 divided by (1 + 7%) raised to the power of 2 is equal to $699. Thus, you have to invest, $699 today to receive $800 in two years. You can solve this with Excel. Let's move to excel and type in numbers. Type in 800 for FV. Type in 7% for rate. Type in 2 for NPER. Type in 0 for PMT. And you'll get PV of $698.75. You can make sure whether your answer is correct by calculating FV using PV you found from Excel. Let's move to Excel and type in the following numbers. Type in 698.75 for PV. Type in 7% for rate. Type in 0 for PMT. Type in 2 for NPER. And you'll get FV of $800. I hope you understand how to calculate the present value now.