1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 3-8 PRESENT VALUE OF INVESTMENTS Calculate the present value of a single deposit investment. Calculate the present value of a periodic deposit investment. OBJECTIVES

2. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Identify whether each graph intersects the x-axis only, the y-axis only, or both axes. 1.y = 3 x 2.y = x 2 + 5x + 6 3.y = 3 Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 present value – current value of a deposit that is made in the present time present value of a single deposit investment – how much a one-time deposit should earn at a specific interest rate in order to have a certain amount of money saved for a future savings goal present value of a periodic deposit investment – how much to save on a regular basis at a specific interest rate to meet that future goal Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 4 Example 1 Mr. and Mrs. Johnson know that in 6 years, their daughter Ann will attend State College. She will need about $20,000 for the first year’s tuition. How much should the Johnsons deposit into an account that yields 5% interest, compounded annually, in order to have that amount? Round your answer to the nearest thousand dollars.

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 How many years would it take for $10,000 to grow to $20,000 in the same account? CHECK YOUR UNDERSTANDING

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 Example 2 Ritika just graduated from college. She wants $100,000 in her savings account after 10 years. How much must she deposit in that account now at a 3.8% interest rate, compounded daily, in order to meet that goal? Round up to the nearest dollar.

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 How does the equation from Example 2 change if the interest is compounded weekly? CHECK YOUR UNDERSTANDING

8. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 EXAMPLE 3 Nick wants to install central air conditioning in his home in 3 years. He estimates the total cost to be $15,000. How much must he deposit monthly into an account that pays 4% interest, compounded monthly, in order to have enough money? Round up to the nearest hundred dollars.

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 Write the formula to find the present value of an x -dollar balance that is reached by periodic investments made semiannually for y years at an interest rate of r. CHECK YOUR UNDERSTANDING

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 EXAMPLE 4 Randy wants to have saved a total of $200,000 by some point in the future. He is willing to set up a direct deposit account with a 4.5% APR, compounded monthly, but is unsure of how much to periodically deposit for varying lengths of time. Graph a present value function to show the present values for Randy’s situation from 12 months to 240 months.

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 Use the graph to estimate how much to deposit each month for 1 year, 10 years, and 20 years. CHECK YOUR UNDERSTANDING

12. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. AssignmentAssignment Page 165, #2 – 10 even Slide 12