1. Warm-ups You deposit $1000 in a savings account that yields 6% simple interest. After two years what is you account balance The balance for years 0, 1 and 2 are $1000, $1060 and $1120. Is this an arithmetic or geometric series. Explain your answer Write a closed form expression for the above case given the general closed form equation A n = A 0 + (n)(d)

2. 7.2 Growth from Money to Moose Compound Interest – When interest is paid on both the principal and the earned interest. Compounded Annually – when the interest on a growth of a savings account is calculate once a year. Multiplicative Model – when the same number gets multiplied repetitively by some initial value.

3. Geometric Sequence – a sequence of numbers that has the property that the ratio btw 2 successive term is constant. Growth Factor – The constant ratio. It is represented by the letter b. Closed form – a n = a 0 ( b ) n Recursive Form – A n = A n-1 * r + A n-1 or

4. 7.2 The Times Are A’ Changin’ Turn to page 402. Complete problems # 1 – 5skip 4! For the table in question 1: ◦ Interest Earned = Beginning Balance*0.05 ◦ Ending Balance = Beginning Balance + Interest ◦ Beginning Balance for year 1 is the Ending Balance for year 0!

5. 7.2 The Times Are A’ Changin’ Annual Interest Model:A = P(b) t where b = 1 + r and is called the growth factor A = Account balance in the future P = principal (initial deposit) r = rate (as a decimal) t = years also written as A = P(1 + r) t Example: If you deposit $300 in an account that pays 5% interest what will the balance be in 10 years? P = 300r = 5% =.05t = 10 Growth factor: b = 1 + r = 1 +.05 = 1.05 A = 300(1.05) 10 = $488.67

6. 7.2 The Times Are A’ Changin’ Annual Interest Model:A = P(b) t also written as A = P(1 + r) t Example: If you deposit $1,000 in an account that pays 9% interest what will the balance be in 5 years? P = 1,000r = 9% =.09t = 5 Growth factor: b = 1 + r = 1 +.09 = 1.09 A = 1,000(1.09) 5 = $1538.62

7. Worksheet Complete the following Millionaire Work sheet

8. 7.2 The Times Are A’ Changin’ Compounding Period: How many times interest is applied to the money in your bank per year. Turn to page 405 and complete question 6. 6 a) interest should be half! b) remember growth factor = 1 + r

9. 7.2 The Times Are A’ Changin’ #6 a) Cut it in half! 6/2 = 3%! b) b = 1 + r = 1 +.03 = 1.03 c) Term Beg. Balance Interest Earned Ending Balance 1rst 6months $1600$48$1648 2 nd 6months $1648$49.44$1697.44

10. 7) to find the ratio = current year’s bal previous year’s bal 1600/1647.44 = 1.0609

11. 7.2 The Times Are A’ Changin’ Turn to page 405 and complete question 7 7 a) Ending Balance = Beginning Balance * 1.03 2 7 b) 1,600*1.03 2 = $1,697.44 7 c) 1,600*1.03 20 = $2,889.78 7 d) calculator....

12. Compound Interest Equation A = P(1 + r/n) nt P : initial deposit or principal sometimes labeled a 0. r : interest rate in decimal form (5% =.05). n : compounding period. How many times interest is applied per year (daily, n = 365). t : years.

13. Examples IF you deposit $100 into and account that pays 7% interest compound quarterly what will the balance be in 20 years? P = 100r = 7% =.07 n = quarterly = 4t = 20 A = P(1 + r/n) nt A = 100(1 +.07/4) (4*20)  parenthesis A = $400.64

14. Examples IF you deposit $500 into and account that pays 5% interest compound monthly what will the balance be in 10 years? P = 500r = 5% =.05 n = monthly = 12t = 10 A = P(1 + r/n) nt A = 500(1 +.05/12) (12*10)  parenthesis A = $823.50

15. Examples IF you deposit $2,000 into and account that pays 2.5% interest compound annually what will the balance be in 5 years? P = 2,000r = 2.5% =.025 n = annually = 1t = 5 A = P(1 + r/n) nt A = 2000(1 +.025/1) (1*5)  parenthesis A = $2,262.82

16. Examples IF you deposit $50 into and account that pays 6.2% interest compound weekly what will the balance be in 15 years? P = 50r = 6.2% =.062 n = weekly = 52t = 15 A = P(1 + r/n) nt A = 50(1 +.062/52) (52*15)  parenthesis A = $126.65

17. Examples How much do you have to deposit into an account that pays 8% interest compounded daily so that in 10 years you have $600? P = ?A = 600r = 8% =.08 n = daily = 365t = 10 A = P(1 + r/n) nt 600 = P(1 +.08/365) (365*10) 600 = P*2.225P = $269.62

18. Examples IF you deposit $430 into and account that pays 4% interest compound three times a year how long until your account has over $1,000? P = 430r = 4% =.04 n = three times = 3t = ? A = P(1 + r/n) nt A = 430(1 +.04/3) (3*t)  parenthesis Guess and check

19. 7.2 The Times Are A’ Changin’ Lets finish this! Turn to page 408 and complete # 9 – 10. When you finish you can start page 410 # 1-4

20. Compound Interest Worksheet

21. Compound Interest Home work Compound Interest worksheet

22. Warm - Up You deposit $500 in an account that pays 2.5% interest every year. 1) What will the balance be in 10 years? 2) How long until the balance doubles? 3) What would you have to deposit initially to have $1,000 in your account after 5 years using the same interest rate?

23. Warm - Up Suppose you deposit $1,000 in a bank account that pays 8% interest per year. What will your balance be in 1 year if….. 1) Your interest is applied once a year. 2) Your interest is applied twice a year (be sure to adjust the interest rate). 3) Your interest is applied four times a year (be sure to adjust the interest rate). 4) How much more interest do you make when applying interest 4 times over a year instead of once?