Simple and Compound Interest

1. Simple and Compound Interest Lesson 9.11

2. REVIEW:Formula for exponential growth or decay Number of times growth or decay occurs Final amount Initial amount Rate of growth or decay 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 depositor 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 Factor out a 100! Number of times growth or decay occurs Final amount Initial amount Rate of growth or decay

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 month After 2 months After 3 months

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

9. Vocabulary • Principal: Amount initially deposited or borrowed. • Intervals for compounding: • Annually – • Monthly – • Weekly – • Daily – • Quarterly – 1 time each year 12 times each year 52 times each year 365 times each year 4 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? Number of times growth or decay occurs Final amount Initial amount Rate of growth or decay

13. Compound Interest as Exponential Growth Total number of times interest calculated Final amount Initial Amount (amount deposited) Rate of growth or decay 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? Total number of times interest calculated 4 times a year for 5 years 20 times! Final amount Initial Amount (amount deposited) Add 1to keep original amount. Annual interest divided into four intervals

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? Total number of times interest calculated 12 times a year for 3 years 36 times! Final amount Initial Amount (amount deposited) Annual interest divided into twelve intervals Add 1to keep original 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 • Determine if you know INITIALor FINAL amount . • Determine the growth rate : • DivideANNUAL rate by the number of intervals each year. • Quarterly: Divide annual by 4. • Weekly: Divide annual by 52 • ADD !!! • Determinenumber of times interest is compounded: • Number of times per year TIMES number of years • Solve for unknown!!

18. Extension Question • How much would Jordan earn in interest? Started with: Ended with: Earned: Interest Earned: