1. 1 Compound Interest Motivation—a choice between two investments (1)Pay $50,000 now for an expected profit of $100,000 after twelve years (2) Invest $50,000 at an interest rate of 7% for twelve years. Which option provides you with the most wealth in twelve years? Need to understand compound interest for an answer.

2. 2 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. TimeFormula for wealth Wealth now50,000 after 1 year50,000 + 50,000(0.07) =50,000(1.07)$53,500

3. 3 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. TimeFormula for wealth Wealth now50,000 after 1 year=50,000(1.07)$53,500 After 2 years={50,000(1.07)}(1.0 7) =50,000(1.07) 2 $57,245

4. 4 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. TimeFormula for wealth Wealth now50,00050,000.00 after 1 year=50,000(1.07)$53,500.00 after 2 years=50,000(1.07) 2 $57,245.00 after 3 years=50,000(1.07) 3 $61,252.15 ……… After 12 years=50,000(1.07) 12 $112,609.58

5. 5 Which option makes us wealthier? (1)Pay $50,000 now for an expected profit of $100,000 after twelve years (2)Invest $50,000 at an interest rate of 7% for twelve years. Provides us with $112,609.58 in twelve years. Clearly this is the better option.

6. 6 Terminology FV = future value PV = present value r = interest rate T = # years What is the future value of $50,000 invested at a 7% interest rate for twelve years? FV = (PV)(1+r) T FV = (50,000)(1.07) 12 FV = $112,609.58

7. 7 More practice What is the future value of $100 invested at a 5% interest rate for 20 years? FV = (PV)(1+r) T FV = (100)(1.05) 20 FV = $265.33 FV = future value PV = present value r = interest rate T = # years

8. 8 Present value FV = future value PV = present value r = interest rate T = # years

9. 9 Present value FV = future value PV = present value r = interest rate T = # years How much money do we need to invest today at an interest rate of 5% to get $265.33 in 20 years?

10. 10 Present value FV = future value PV = present value r = interest rate T = # years How much money do we need to invest today at an interest rate of 3% to get $40,000 in 5 years?

11. 11 Back to the original question (1)Pay $50,000 now for an expected profit of $100,000 after twelve years. How much money do we need to invest today at 7% interest to receive $100,000 after 12 years? PV = (100,000)(1.07) -12 = $44,401.20 Clearly we prefer $50,000 dollars today over $44,401.20 dollars today. It’s a bad investment.