1. Interest and Depreciation R o b y n F a r r e l l, J o h n D o v a n, L i w e n Y u.

2. What is Interest? Interest is the number gained when money is invested. For example, if you have $100 invested, and the interest rate is 3%, you would gain 3% of a 100 each year ($3) For example, if you have $100 invested, and the interest rate is 3%, you would gain 3% of a 100 each year ($3)

3. Using exponentials to Model Compound Interest The formula for an a bank account that is compounded monthly, yearly, quarterly, etc is modeled below. A= the balance of the account P= the initial amount r= the interest rate (as a decimal) n= the number of times the interest is compounded yearly t= the number of years the account has been active Here’s a tip: Be on the look out for the words, monthly, annually, quarterly, etc!

4. Examples With 1D. Harry Styles has $2000 and opened a bank account at Citizens Bank. The bank offers an interest compounded monthly of 3.2%. How much money will Harry have in his bank account after 6 years? In 6 Years, Harry will have $2422.72.

5. Try one for yourself! Zayn Malik has a bank account with $20,451 with an interest rate of 2.3% compounded quarterly. Liam Payne also opened a bank account with $19,750 with a monthly interest of 3.4%. Write an equation that models these situations. Make a table of 10 values and graph the values. Who will reach $45,000 first?

6. Are you right? 0123456789 $2045 1 209252141121908224162293623468240122456925139 Z= 0123456789 $1975020432211382186822623234042421225049259142680 9 L= Louis will reach $45000 before Zayn. Wait up! This looks familiar. OH! It’s the base change formula!

7. Using Exponentials to Model Compound Interest In situations when an interest rate is compounded continuously, use the following equation: A= the balance of the account P= the initial amount e= Euler’s number (the natural base, 2.718) r= the interest rate (as a decimal) t= the number of years the account has been active Pstt! Only use this when it is CONTINUOUSLY!

8. Example with Rebecca Black. After the smash hit of “Friday”, Rebecca Black made millions of dollars, but she decided to only invest $15,250 in a bank account. It comes with an interest rate of 5.7% that is compounded continuously. Write an equation to model this situation. How much money will she have by the end of 2 years? In 2 years, Rebecca will have $17,611.72 in her bank account.

9. Do it yourself! John opened a bank account with $2,300 that has an interest rate of 2.3% which is compounded continuously. Write an equation. How long will it take John to have $6,000 in his bank account?

10. Check your work! It will take John about 42 years to have $6000 in his bank account.

11. What is depreciation? Depreciation is to loose value over a certain amount of time. A popular example of this is…. CARS! Once you drive a new car, it immediately loses value.

12. Using Exponents to Model Depreciating Value To model these examples use the equation: Insert equation V(t)= the value of the object after t years V 0 = the initial value of the object r= the percent of decrease per year (as a decimal of course!) t= number of years since the object was purchased

13. Example with Snooki. Snooki just purchased a Ford 2012 Focus for $18,300. But it’s value depreciates by 11% each year. Write an equation modeling this situation. What is the value of her Ford Focus if 5 years passed? Her Ford Focus will be worth $10,218.83 in 5 years.

14. Do it yourself! Christine bought a new iPhone 4S costing $300. After a new iPhone came out the value started deprecating by 15% yearly. Write an equation I only have $1. How long will take for me to buy her iPhone with the money I have?

15. How did you do? It will take about 35 years for the iPhone to be worth $1.

16. The End c: How did we do? Give us your feedback! If you have any questions feel free to message us on Facebook!