Download presentation
Presentation is loading. Please wait.
Published byBrooke Miles Modified over 8 years ago
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!
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.