1. Happy Tuesday! Do the following: Warm-up
Clear your desks and be ready for the quiz!!!!!!
Warm-up
 No warm-up. The quiz is your warm-up.
HW #5:
P 346 #7, 13, 15, 23, 25, 31, 35, 39, 53 ( you need a calculator for these problems… can download a free graphing calculator app) Begin Study Guide

2. Happy Tuesday! Do the following: Warm-up
Clear your desks and be ready for the quiz!!!!!!
Warm-up
 No warm-up. The quiz is your warm-up.
HW #5:
Finish Example 4
P 346 #7, 13, 15 ( you need a calculator for these problems… can download a free graphing calculator app) Begin Study Guide

3. Office Hours!
After school on Thursday .
Lunch everyday
1 min

4. Agenda
Warm-Up!
Review HW
4.6 Quiz
Finish 4.7 Notes

5. Go Over HW
p 337 # 5-21 odd ( skip 15) , 33,41, 43, 47

6. 4.6 Quiz This is going to be two problems from your 4.6 notes.
No TALKING, CALCULATOR OR NOTES!
Cover your paper and turn it in when you are done.
1 min

7. Looking Ahead… Tues/Wed 4.7 Thurs/Fri: Finish 4.7 Start 4.8
Monday/Tues
Finish 4.8 and begin Review
Wed/Thursday
Review in Class
Wednesday/Thurs after school study session from 3:30-4:30
Fri- Wed
EXAM 3

8. How to Study?!?!
Study groups ( get someone's phone number from the class and meet up over the weekend)
Do the homework and example problems over again
Khan Academy
Do the practice review problems that I gave you and check your solution!!! (don’t just copy the solution, but make sure you know how to do it!)
Remember! This review is not exactly like every Exam 2 Problem. Math 111 requires mastery of the concepts, not a memorization of procedures.

9. Learning Objectives By the end of the period you will be able to:
Solve log equations

10. Calculator Expectations
The next week we are going to use calculators.
The resource manager is going to come up and get the calcs.
TABLE #1 ( CALCS #1-4)
TABLE #2 ( CALCS 5- 8)
TABLE #3 ( CALCS 9-12)
TABLE #4 ( CALCS )
TABLE #5 ( CALCS )
TABLE #6 ( CALCS )
TABLE #7 ( CALCS )
5 minutes before the bell rings, the resources manager is going to put the calcs away in the designated spot!!!
NO ONE LEAVES MY CLASS UNTIL ALL CALCULATORS ARE PUT AWAY!!!!
1 min

11. Many financial models use exponential functions.
Let’s apply what we have learned to what everyone loves: $$$$$$$$$$$$$$$ !

12. Open Notebook
Title Notes to: 4.7: Financial Models

13. 4.7: Financial Models Compound Interest A = final amount ($)
P = initial amount or principal
r = annual interest rate(%)
n = number of times the interest is compounded per year
t = time in years

14. 4.7: Financial Models Common Compounding Periods
n is the number of times the interest is compounded per year
annually, n =
semiannually, n =
monthly , n =
quarterly, n =
daily, n =

15. Hint: When putting this in your calculator remember parentheses!!!
Example 1-on Packet
Example 1: Find the Future Value of a Lump Sum of Money
Use the compound interest formula to calculate the amount of money you would have after 5 year if you invest $300 at an annual rate of 4.3% compounded:
(a) Annually (c) Monthly
(b) Quarterly (d) Daily
What do you notice as you increase n?
Hint: When putting this in your calculator remember parentheses!!!

16. 4.7: Financial Models
Assume that you have $1 and it earns 100% annual interest. This table shows the growth factor for each of the compounding frequencies listed.

17. 4.7: Financial Models Continuously Compounded Interest A = Pert
A = final amount ($)
P = initial amount (principal)
r = annual interest rate(%)
t = time in years
Continuously Compounded interest is when interest (a fee) is added to a deposit or loan, so that, from that moment on, the interest that has been added also earns interest.
It is different from the compounded interest formula

18. Example 2-on Packet Example 2: Continuous Compounding
How much money will your credit card have after loaning you $5000 at 11.9% interest compounded continuously for 4 years? How much of that is just interest?

19. Example 3-on Packet
Congrats! You just won the lottery! You are smart and going to invest your money for 30 years. However, you are debating on whether to invest your $50,000 winnings into a money market that earns 8.5% interest compounded quarterly or into a savings account that earns 7.9% interest compounded continuously. Which option would you choose and why?

20. Whiteboards
Compare the balance after 25 years of a $10,000 investment earning 6.75% interest compounded continuously to the same investment semiannually. Which option would you choose?
Coninuously

21. Financial Models Table- Talk:
Discuss the difference between interest compounded continuously and interest compounded monthly.
If you have an investment compounded daily OR you have an investment compounded continuously, does it matter which formula that you use?

22. Financial Models “How long will it take…” Example
You invest $5,000 into an account with interest rate of 2.25% compounded daily.
(a) Write the formula that models the value of the investment after t years? (b) How long will it take for the account value to reach $15,000?
How long will it take for the account value to reach $20,000?

23. Example 4
Example 4: You invest $8,000 into an account with interest rate of 4% compounded monthly.
Write the formula that models the value of the investment after t years?
What will the value of this investment be after 10 years?
How long will it take for the account value to reach $20,000?

24. Financial Models Interest to Double or Triple Money
(a) What interest rate ( compounded continuously) is required for the value of an investment to double in 10 years?

25. Financial Models Interest to Double or Triple Money
 (b) What interest rate ( compounded annually) is required for the value of an investment to triple in 15 years?

26. Example 5- on Packet
(a) What interest rate ( compounded continuously) is required for the value of an investment to double in 15 years?
 (b) What interest rate ( compounded annually) is required for the value of an investment to triple in 15 years?

27. Financial Models Effective Rate of Interest “which is the better deal”
Interest rate that is equivalent to compounding n times per year or continuously after 1 year
Higher the interest the better deal