1. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.0 Future Values Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? Interest = 1000(.05) = 50 Value in one year = principal + interest = 1000 + 50 = 1050 Future Value (FV) = 1000(1 +.05) = 1050 Suppose you leave the money in for another year. How much will you have two years from now? FV = 1000(1.05)(1.05) = 1000(1.05) 2 = 1102.50

2. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.1 Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of.05(50) = 2.50 earned on the first interest payment

3. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.2 Future Values – Example 3 Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? FV = 10(1.055) 200 = 447,189.84 What is the effect of compounding? Simple interest = 10 + 200(10)(.055) = 210.55 Compounding added $446,979.29 to the value of the investment

4. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.3 Present Values How much do I have to invest today to have some amount in the future? FV = PV(1 + r) t Rearrange to solve for PV = FV / (1 + r) t There are four parts to this equation PV, FV, r and t If we know any three, we can solve for the fourth When we talk about discounting, we mean finding the present value of some future amount.

5. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.4 PV – One Period Example Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today? PV = 10,000 / (1.07) 1 = 9345.79 Calculator 1 N 7 I/Y 10,000 FV PV = -9345.79

6. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.5 Present Values – Example 1 You want to begin saving for you daughter’s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today? PV = 150,000 / (1.08) 17 = 40,540.34 Calculator 17 N 8 I/Y 150,000 FV PV -40,540.34

7. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.6 Present Values – Example 2 Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest? PV = 19,671.51 / (1.07) 10 = 10,000 Financial Calculator 19,671.51 FV 7 I/YR 10 N PV

8. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.7 Discount Rate – Example 1 You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest? r = (1200 / 1000) 1/5 – 1 =.03714 = 3.714% Calculator – the sign convention matters!!! 5 N 1000 +/- PV (you pay 1000 today) 1200 FV (you receive 1200 in 5 years) I/Y Answer 3.714%

9. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.8 Discount Rate – Example 2 Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest? r = (20,000 / 10,000) 1/6 – 1 =.122462 = 12.25% Calculator 6 N 1000 +/- PV 20,000 FV I/Y

10. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.9 Discount Rate – Example 3 Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5000 to invest. What interest rate must you earn to have the $75,000 when you need it? r = (75,000 / 5,000) 1/17 – 1 =.172688 = 17.27% Calculator 17 N 5,000 +/- PV 75,000 FV I/Y

11. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.10 Number of Periods – Example 1 You want to purchase a new car and you are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car? t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years Calculator 10 I/Y 15,000 +/- PV 20,000 FV N

12. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.11 Multiple Cash Flows – FV Example 1 Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years? FV = 500(1.09) 2 + 600(1.09) = 1248.05 How much will you have in 5 years if you make no further deposits? First way: FV = 500(1.09) 5 + 600(1.09) 4 = 1616.26 Second way – use value at year 2: FV = 1248.05(1.09) 3 = 1616.26

13. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.12 Multiple Cash Flows – PV Another Example You are considering an investment that will pay you $1000 in one year, $2000 in two years and $3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? PV = 1000 / (1.1) 1 = 909.09 PV = 2000 / (1.1) 2 = 1652.89 PV = 3000 / (1.1) 3 = 2253.94 PV = 909.09 + 1652.89 + 2253.94 = 4815.93

14. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.13 Annuity – Sweepstakes Example Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today? PV = 333,333.33[1 – 1/1.05 30 ] /.05 = 5,124,150.29 Financial Calculator 333,333.33 PMT; 5 I/YR; 30 N; PV

15. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.14 Finding the Payment Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 =.66667% per month). If you take a 4 year loan, what is your monthly payment? 20,000 = C[1 – 1 / 1.0066667 48 ] /.0066667 C = 488.26 Financial Calculator 20,000 PV; 48 N;.6666 I/YR; PMT

16. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.15 Finding the Number of Payments – Another Example Suppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan? 2000 = 734.42(1 – 1/1.05 t ) /.05.136161869 = 1 – 1/1.05 t 1/1.05 t =.863838131 1.157624287 = 1.05 t t = ln(1.157624287) / ln(1.05) = 3 years Financial Calculator $2000 PV; 734.42 +/- PMT; 5 I/YR; N

17. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.16 Finding the Rate Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? Sign convention matters!!! 60 N 10,000 PV -207.58 PMT I/Y =.75%

18. McGraw-Hill © 2004 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5.17 Future Values for Annuities Suppose you begin saving for your retirement by depositing $2000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years? FV = 2000(1.075 40 – 1)/.075 = 454,513.04 Financial Calculator -2000 PMT (use +/- key to change sign) 40 N 7.5 I/YR FV = $454,513.03