Copyright © 2011 Pearson Education, Inc. Managing Your Money

Copyright © 2011 Pearson Education, Inc. Slide 4-3 Unit 4B The Power of Compounding

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-4 Definitions The principal in financial formulas is the balance upon which interest is paid. Simple interest is interest paid only on the original principal, and not on any interest added at later dates. Compound interest is interest paid on both the original principal and on all interest that has been added to the original principal.

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-5 A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) Y = number of years Compound Interest Formula for Interest Paid Once a Year

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-6 Simple and Compound Interest Compare the growth in a $100 investment for 5 years at 10% simple interest per year and at 10% interest compounded annually. The compound interest account earns $11.05 more than the simple interest account.

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-7 4B Part 2: The Power of Compounding CN 1- Definitions: Present value is the original principal. Future value is the accumulated amount.

4-B p.216 Compound Interest paid more than once a year Suppose you deposit $1000 into a bank that pays compound interest at an annual percentage rate of APR = 8%. Copyright © 2011 Pearson Education, Inc. Slide 4-8

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-9 Compound Interest Show how quarterly compounding affects a $1000 investment at 8% per year.

4-B In other words…. We see that if interest is paid quarterly, the interest rate at each payment is APR/4. Generalizing, if interest is paid n times per year, the interest rate at each payment is APR/n. The total number of times that interest is paid after Y years is nY. Copyright © 2011 Pearson Education, Inc. Slide 4-10

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-11 A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) n = number of compounding periods per year Y = number of years Compound Interest Formula for Interest Paid n Times per Year

4-B CN (1-2) You deposit $5000 in a bank account that pays an APR of 3% and compounds interest monthly. 1. How much money will you have after 5 years? 2. Compare this amount to the amount you’d have if interest were paid only once each year. Copyright © 2011 Pearson Education, Inc. Slide 4-12

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-13 Definition The annual percentage yield (APY) is the actual percentage by which a balance increases in one year. It is sometimes also called the effective yield or simply the yield. APY = relative increase = absolute increase starting principal

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-14 APR vs. APY APR = annual percentage rate APY = annual percentage yield APY = APR if interest is compounded annually APY > APR if interest is compounded more than once a year

4-B FYI Banks usually list both the annual percentage rate (APR) and the annual percentage yield (APY). However the APY is what your money really earns and is the more important number when you are comparing interest rates. Banks are required by law to state the APY on interest-bearing accounts. Copyright © 2011 Pearson Education, Inc. Slide 4-15

4-B More Compounding means higher yield CN (3-4) You deposit $1000 into an account with APR = 8%. Find the annual percentage yield with: 3. monthly compounding and with 4. daily compounding Copyright © 2011 Pearson Education, Inc. Slide 4-16

4-B Continuous Compounding CN (5) Suppose that interest were compounded more often than daily – say, every second or every trillionth of a second. 5. How would this affect the annual percentage yield? More frequent compounding means a higher APY. The change gets smaller as the frequency of compounding increases. APY can’t get much bigger than it already is for daily compounding? Copyright © 2011 Pearson Education, Inc. Slide 4-17

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-18 Continuous Compounding Show how different compounding periods affect the APY for an APR of 8%.

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-19 Continuous Compounding

4-B Copyright © 2011 Pearson Education, Inc. Slide 4-20 A = accumulated balance after Y years P = starting principal APR = annual percentage rate (as a decimal) Y = number of years = a special irrational number with a value of Compound Interest Formula for Continuous Compounding

4-B CN (6) You deposit $100 in an account with an APR of 8% and continuous compounding. 6. How much will you have after 10 years? Copyright © 2011 Pearson Education, Inc. Slide 4-21

4-B College Fund for baby at 3% CN (7) Suppose you put money in an investment with an interest rate of APR = 3%, compounded annually, and leave it there for the next 18 years. 7. How much would you have to deposit now to realize $100,000 after 18 years? Copyright © 2011 Pearson Education, Inc. Slide 4-22

4-B College Fund at 5% compounded monthly CN (8) Repeat the same as last problem, only at 5% and monthly compounding. 8. How much would you have to deposit now to realize $100,000 after 18 years? Copyright © 2011 Pearson Education, Inc. Slide 4-23

4-B A brief review of Algebra CN (9-11) 9. The Three Basic Rules Add or subtract same quantity on both sides Mult. or divide on both sides (no div. by zero) You can interchange the left and right sides of equation 10. Adding and Subtracting (examples) Add or subtract from both sides, or interchange to help find answer 11. Multiplying and Dividing (examples) Cannot isolate a variable by add or subtract alone, may need to mult. or divide both sides of equation Copyright © 2011 Pearson Education, Inc. Slide 4-24

4-B 4B Part 2 Homework 4B part 2: p.224: even 1 web (95) 1 world (96 or 97) Copyright © 2011 Pearson Education, Inc. Slide 4-25