Unit 5: Exponentials

Lesson 2: Bank Investments

Objectives:

  • I understanding the different banking investment options
  • I can evaluate the amount of money generated from using different investment options
  • I canwrite and evaluate exponential functions

Agenda:

  • Warm up: Round 1: Remembering our midterm

Round 2: Graphing and analyzing exponential functions

  • Banking and investment options
  • Practice investment problems

Focus Questions:

  • What is Simple interest and compounded interest?
  • Which banking investment option generates more money?
  • How can I calculate the amount of money I can make from these investment options?

Vocabulary:

  • Simple interest
  • Compounded interest
  • Quarterly
  • Depreciates

Homework: HW 5-2

Warm up:Round 1:Remembering the Midterm

  1. The length of a rectangular door is 5 feet more than its width, w. The area of the door is 36 square feet. Write an equation which could be used to find the dimensions of the door? Find the door’s dimensions. Only an algebraic solution will be accepted.
  1. Graph the following exponential function:

On the integral. What is an appropriate range

Determine whether this function is

Growth or decay?

  1. What is the initial value for this function when x=0?
  1. What is the rate of change for this function on that interval?
  1. Describe the transformation after

3) Factoring: (5 min)

A)
v2 – 7v + 10 / B)
p2 + 3p –18 / C)
6v2 + 66v + 60
D)
v2 – 7v / E)
3p – 18 / F)
6v2 - 600

4)If m(x) = Solve for x when m(x) = 0.

5)The breakdown of a sample of a chemical compound is represented by the function p(t) = 300, where p(t) represents the number of milligrams of the substance and t represents the time, in years.

In the function p(t), explain what 0.5 and 300 represent

When do we ever need this? Banking and Interest Rates

Banks pay customers interest to look after their money. When you invest your money in a bank, you have many investment options that you can choose from. In banking the starting amount of money is usually called the principle and donated by (P). (A) is the final balance, (r) is the interest rate, and (n) is the number of times the money compounded.

Most Banks offer the following investment account options for their customer

Compounded / Value of n / Formula used
Simple Interest – Interest is calculated once per year on the original amount borrowed or invested. The interest does not become part of the amount borrowed or owed (the principal). / N/A /
Compound Interest –Interest is calculated once per period on the current amount borrowed or invested. Each period, the interest becomes a part of the principal.
Money can be compounded: /
Yearly / n=1
Quarterly / n=4
Monthly / n=12
Daily / n=365
Weekly / n=52

Example 1:Caroline deposited $1500 in an account that pays 4% interest compounded quarterly. What will the balance be in 2 years?

Example 2:Tinny’s have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the total balance after three years.

Discuss your options:

2)If you have $???to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually?

3)Student Friendly Bank pays a simple interest rate of 2.5% per year. neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly. Which bank will provide the largest balance

a. If you plan to invest $??, ???for 10 years?

b. For 20 years?

c. Estimate when the first option will generate at least $14000?

Mathematician: ______Algebra I

Homework 5-2

1) A construction company purchased some equipment costing $????. The value of the equipment depreciates (decreases) at a rate of ??% per year.

a. Write a function that models the value of the equipmentV(t)over the years (t).

b. What is the value of the equipment after ?years?

c. Graph the points (?,V(?))for integer values of ?≤?≤??.

d. Estimate when the equipment will have a value of $??,.

1)Sam bought a used car for $8,000. He believes that he got a great deal since the value of the car two years ago (when it was new) was $15,000. His friend, Derek, was skeptical, stating that the value of a car typically depreciates about ??% per year, so Sam got a bad deal. Who is right, Sam or Derek? Why?

2)Courtney opens a savings account by depositing $1200 in an account that earns 3% interest compounded quarty. How much will her investment be worth in 10 years?

3James needs $200 to start a snow cone stand for this hot summer. He borrows the money from a bank that charges 4% simple interest a year.

  1. Write down the equation that will help you identify the money earned f(x) after x years?
  1. How much will he owe if he waits 1 year to pay back the loan?
  1. If he waits two years? 3 years?

4)The Green’s Construction Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 2% interest compounded quarterly. If an employee works with the company for five years, how much money will he have in his account?

Have you worked on your take home quiz questions?