Logarithm Project Unit 5 – Exponential Growth and Decay/ Compound Interest

Using your knowledge of exponential functions, create a mini poster with the following criteria.

PART I: You are buying a new car! Before you do that, you need to do some comparisons to show which scenario is the better deal.

Find a new car that you would like to buy. (Find a picture)

Research the list price of the car.

Scenario 1:You can get a 60 month (5 year) payment plan, where your APR for the payments will be 3.9% and it is compounded monthly. (Use the price you found.) Show work and equations.

How much more will you pay for the car than the list price?

How much would you save if you paid off the car in 2 years?

Scenario 2:The dealership offers an option of taking $3,000 off the list price but charging 6.9% APR for 5 years compounded monthly. Show work and equations.

Which scenario is the better deal?

PART II: Find another car that costs between $10,000-$15,000. (Find a picture)

You are now looking at a car that costs $10,000-$15,000 to pay off over 5 years.  You know that you DON’T want to pay more than a total of $20,000.  What is the highest interest rate you will be willing to pay?

PART III: You have decided that you want to trade in your car when the value is no less than $5,000 – you want a down payment for your next car! According to bankrate.com, cars lose between 15% and 20% of their value each year.  How many years will it be until your car is worth $5,000?

Part IV: You open a savings account that gets compounded monthly at 18%. How much do you need to deposit to save up for the car in option 2 is you save for 2 years?

Criteria Points Possible Points EarnedPicture of New Car 3List Price 3Part 1 Scenario 1 (Both parts worked out)

10

Scenario 2 (Worked out) 10Which is a better deal (stated) 3Picture of 2nd car 3List Price 3Part 2 Rate problem  (Worked out) 20Part 3 Selling car problem (Worked out) 20Part 4 savings account (worked out) 20

Neatness 5Total 100

Car project work space:PART I: Researching car/ comparing compound interest

Scenario 1:

Growth function to show how much you are paying for the car after x years________________________________

how much would you have to pay if you paid it off in 5 years?________________________

How much more is that than the original list price?______________________________?

Show work:

How much would you have to pay if you paid it off in 2 years?_______________________

How much more is that than the original list price?_____________________________

Show work:

How much would you save if you paid it off in 2 years instead of 5?_______________________

Show work:

Scenario 2:

Subtract $3,000 from original list price___________________________

Write the equation for this scenario p= n= r= t= ______________________________________.

How much would you pay for this scenario?______________________________

Which scenario is the better deal and why?________________________________________________

PART II Interest rate:

Type of car: ______________________________

List price:________________________________

Write the equation to find the interest rate A= P= t= n= ___________________________show work:

Highest interest rate_________________

PART III Selling:

Choose a depreciation rate between 15-20% _____________________________.

Write the decay function using the rate from above for x years________________________________

Using the table in the calculator, write the largest year number where the car is still worth at least $5000____________.

Part IV: Savings account Write out the compound continuous formula________________________

A= r= t=

How much would you have to deposit?_______________________