1. Simple and Compound Interest Lesson 9.11

2. REVIEW: Formula for exponential growth or decay Initial amount Rate of growth or decay Number of times growth or decay occurs Final amount REMINDER: Percentage increase is 1 + rate of increase. Percentage decrease is 1 – rate of decrease.

3. Interest (one type of exponential growth)  Money you earn (savings account, CD, etc.) or pay (car loan, student loan, mortgage)  Percentage of the initial deposit or loan.

4. Simple Interest Example #1  Calculated ONE time. You lend $100 to your little brother. He will pay you back in one year, with simple interest of 10%. How much will your brother pay you back? Original amount Interest Your little brother will pay you back $110.

5. Simple Interest as Exponential Growth Initial amountRate of growth or decay Number of times growth or decay occurs Final amount Factor out a 100!

6. Compound Interest  Calculated at specific intervals (earn interest on interest)  Annual interest rate is divided among these intervals. You put $100 in the bank. The bank also pays 10% annual interest, but this interest is compounded monthly. After 1 month After 2 months After 3 months

7. Compound Interest Formula After 1 monthAfter 2 monthsAfter 3 months

8. Compound Interest Formula A = Final amount P = Principal (initial amount) interest rate (r) divided by number of times compounded in a year (n) # of times compounded in a year (n) times the #of years (t).

9. Vocabulary  Principal: Amount initially deposited or borrowed.  Intervals for compounding:  Annually –  Monthly –  Weekly –  Daily –  Quarterly – 1 time each year 4 times each year 12 times each year 52 times each year 365 times each year

10. Check for Understanding  Independently annotate your notes  Your notes should be able to answer:  What is simple interest?  What is compound interest?  What are the formulas for each type of interest?  Explain how to derive the formula for compound interest.

11. Backup

12. You put $100 in the bank. The bank also pays 10% interest, but this interest is compounded monthly. How much will you earn after 3 months? Initial amount Rate of growth or decay Number of times growth or decay occurs Final amount

13. Compound Interest as Exponential Growth Initial Amount (amount deposited) Rate of growth or decay Total number of times interest calculated Final amount part of annual interest paid each time

14. Example #3:  You put $1200 in a certificate of deposit account (CD). This CD pays 4% annual interest, compounded quarterly, for 5 years. How much money will be in your account at the end of 5 years? Initial Amount (amount deposited) Annual interest divided into four intervals Add 1to keep original amount. Final amount

15. Example #4:  Jordan plans to purchase a brand new apple computer to bring to college. The I-Mac she wants is projected to cost $1500 at the time of her graduation in 2017. She found an account that pays 2.5% interest, compounded monthly. How much money should Jordan deposit this July, to make sure she has enough money to buy the I-Mac in June of 2017? Initial Amount (amount deposited) Annual interest divided into twelve intervals Add 1to keep original amount. Final amount

16. Jordan must deposit about $1391.72 this July to have enough money to buy the I-Mac in June of 2015.

17. Process

18. Extension Question  How much would Jordan earn in interest?