1. Module 24: The Time Value of Money Present Value : The use of interest rates to compare the value of a dollar realized today with the value of a dollar realized later. https://www.youtube.com/watch?v=TRTkCHE 1sS4 https://www.youtube.com/watch?v=TRTkCHE 1sS4

2. Borrowing, Lending, and Interest Suppose you lend your friend $100, and he is going to pay you back in 1 year. Assume no inflation and interest rate of 10% How much will you receive? Repayment on lending $100 for one year= $100 + $100*.10=$100*(1+.10) = $110 Let’s look at the formulas

3. Defining Present Value Defining Present Value Let Fv = future value of $ Pv = present value of $ r = real interest rate n = # of years The Simple Interest Formula Fv = PV x ( 1 + r ) n Pv = fv / (1 + r) n

4. Application of the formula Using the formula fv = (1 + r) * pv in a one year example with $100 at 10% FV = $100*(1.10) = $110 So, one year in the future, $100 in the present will be worth $110. Now let’s lend the money for a period of 2 years: Repayment in two years = $100(1.10)*(1.10) = $121 FV = PV(1+r)*(1+r) = PV(1+r) 2 Money today has more value than same amount in the future. Interest paid on savings and interest charged on borrowing is designed to equate the value of dollars today with the value of future dollars.

5. Using Present Value Using Present Value

6. Expected Real Rate of Return vs. Real Rate of Interest A local pizza parlor invests $10,000 in a new delivery car. The owner expects this to help to deliver more pizzas, increasing revenues and profits. The car lasts exactly one year and the increased real profits are anticipated to be $2000. This expected real rate of return is $2000/$10,000=.20 or 20 percent. The owner goes to the bank and asks for a one-year loan to purchase the new delivery car. The bank offers a nominal rate of interest of 15 percent; this includes 5% for expected inflation and 10% as the real rate of borrowing the money for a year. At the end of the year, he spends $1000 as real interest on the $10,000 loan. The Decision: Since the new delivery car provides $2000 in additional real profits (r=20%) and the loan cost $1000 in real interest (i=10%), this investment should be made. HINT: If r% ≥i% make the investment. If r% ≤ i% do not make the investment

7. Question: Review What is the amount you will receive in 3 years if you loan $1000 at 5 % interest? $1,000 x (1.05) 3 =$1,000 x1.16 =$1,157.63 Homework: Complete the Time Value of Money assignment. You will get this on the first day back.