Example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8%

Slides:

Advertisements

Similar presentations

Example 1 Matrix Solution of Linear Systems Chapter 7.2 Use matrix row operations to solve the system of equations  2009 PBLPathways.

Advertisements

Example 3 Inverse of a 3 x 3 Matrix Chapter 7.4 Find the inverse of.  2009 PBLPathways.

Example 2 Finding an Inverse Matrix Chapter 7.4 Find the inverse of.  2009 PBLPathways.

Example 1 Solution by Elimination Chapter 7.1 Solve the system  2009 PBLPathways.

Equation of a Tangent Line

Example 3 Peanut Production Chapter 4.2 Georgia’s production of peanuts has increased moderately in the last 10 years, but profit margins have been reduced.

Example 4 Home Mortgage Chapter 5.6 A couple who wants to purchase a home has $30,000 for a down payment and wants to make monthly payments of $2200. If.

Saving and Interest February Saving and Interest An Equation to define Savings: – SAVING = Disposable Income – Consumption. Interest: – Simple Interest.

CONTINUOUSLY COMPOUNDED INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years)

What is Interest? Interest is the amount earned on an investment or an account. Annually: A = P(1 + r) t P = principal amount (the initial amount you borrow.

Example 2 Future Value of an Annuity Chapter 5.6 Harry deposits $200 at the end of each month into an account that pays interest 12% per year, compounded.

Example 5 Inmate Population Chapter 1.4 The number of people (in millions) in U.S. prisons or jails grew at a constant rate from 1990 to 2000, with 1.15.

Example 2 Depreciation Chapter 8.4 An automobile valued at $24,000 is depreciated over 5 years with the sum-of-the-years- digits depreciation method. Under.

Section 6.7 Compound Interest. Find the amount A that results from investing a principal P of $2000 at an annual rate r of 8% compounded continuously.

Models of Exponential and Log Functions Properties of Logarithms Solving Exponential and Log Functions Exponential Growth and Decay

Example 2 Investment Chapter 7.2 The Trust Department of Century Bank divided a $150,000 investment among three mutual funds with different levels of risk.

Exponential Growth & Decay in Real-Life Chapters 8.1 & 8.2.

AP Calculus Ms. Battaglia. Solve the differential equation.

Objectives  Find future value of investments when interest is compounded n times per year  Find future value of investments when interest is compounded.

Example 6 Solution of Exponential Equations Chapter 5.3 Solve the following exponential equations: a. b.  2009 PBLPathways.

Warm Up In the textbook… p. 436 #1 – 3 Read directions about x values!

Understanding Interest Business Economics. Why Interest? Nothing in this world is free. Banks wouldn’t make money People wouldn’t make money Businesses.

Section 6.3 Compound Interest and Continuous Growth.

Compound Interest 8.2 Part 2. Compound Interest A = final amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of.

Example 3 Height of a Ball Chapter 3.1 A ball is thrown at 64 feet per second from the top of an 80-foot-high building. a.Write the quadratic function.

Example 3 Average Cost Chapter 6.5 a.Graph the function on the window [-20, 20] by [-30, 50]. b.Does the graph in (a) have a horizontal asymptote? c.Graph.

Chapter 10: Compound Interest, Future Value, and Present Value  Find the future value and compound interest by compounding manually.  Find the future.

Real Exponents Chapter 11 Section 1. 2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is.

Investment (pg. 506 #30)Investment (pg. 506 #30) A trust account manager has $500,000 to pay 8%, 10%, and 14% respectively, and the goal is to earn $49,000,

Example 6 Internet Use Chapter 4.4 According to Internet World Stats, the number of worldwide Internet users, in millions, during the years 1995 to 2007.

Example 4 Continuous Versus Annual Compounding of Interest Chapter 5.5 a.For each of 9 years, compare the future value of an investment of $1000 at 8%

– The Number e and the Function e x Objectives: You should be able to… 1. Use compound interest formulas to solve real-life problems.

8 th Grade Math Chapter 2 Review. Chapter 2 Review 1)Use >, < or = to compare a) -7 < 7 b) -3 < -1 □ □

example 3 Blood Alcohol Percent

Example 3 Finding an Inverse Function Chapter 4.3 a.Find the inverse function of. b.Graph and its inverse function on the same axes.  2009 PBLPathways.

Math – Solving Problems Involving Interest 1.

You deposit $950 into an account that earns 4 % interest compounded annually. Find the balance in the account after five years. In your last calculation,

Section 5.5 Exponential Functions and Investing Copyright ©2013 Pearson Education, Inc.

Example 8 Stock Prices Chapter 6.3 The closing price of a share of Worldcom, Inc. stock for the years 1994–2000 can be modeled by the equation where x.

Find the amount after 7 years if $100 is invested at an interest rate of 13% per year if it is a. compounded annually b. compounded quarterly.

Compound Interest Formula. Compound interest arises when interest is added to the principal, so that, from that moment on, the interest that has been.

Example 2 Average Cost Chapter 6.6 The average cost per set for the production of 42-inch plasma televisions is given by where x is the number of hundreds.

Compound Interest. interest that actually earns interest itself to figure: –find the initial interest –add it to the principal –find the interest on the.

Bellringer Calculate the Simple Interest for #s 1 and 3 and the Total cost for #2. 1.$1800 at 3.2% for 4 years. 2. $17250 at 7.5% for 6 years. 3. $3,650.

Example 3 Alcohol-Related Deaths Chapter 6.2 The table gives the number of thousands of people killed in alcohol-related traffic accidents for the years.

Example 1 Solving a Nonlinear System Algebraically Chapter 7.5 Use substitution to solve the system and check the solution.  2009 PBLPathways.

Math 1320 Chapter 2: The Mathematics of Finance 2.2 Compound Interest.

Example 1 Graph of an Inequality Chapter 8.1 Graph the solution of the inequality.  2009 PBLPathways.

Bellwork 1. Solve for x. 2. Write in logarithmic form: 3. Write in exponential form: ln = 7 Evaluate and simplify if possible

THE TIME VALUE OF MONEY “A Dollar Today is Worth More than a Dollar Tomorrow”

INTEREST. Simple Interest Compound Interest SIMPLE INTEREST VS. COMPOUND INTEREST Interest earned on the principal investment Earning interest on interest.

3.5 Exponential and Logarithmic Models n compoundings per yearContinuous Compounding.

CHAPTER 5 LESSON 5 Exponential Functions and Investing.

Simple Interest The simple interest formula is often abbreviated in this form: I = P R T Three other variations of this formula are used to find P, R and.

Future Value of an Investment

SIMPLE AND COMPOUND INTEREST

CDs and Annual Yield Lesson 7.3.

the square root principal and completing the square

Chapter 7 Jeopardy! Solving Equations

Unit 4: Financial Applications MAP 4C

CHAPTER TEN COMPOUND INTEREST.

3.5 Exponential Growth & Decay

Simple and Compound Interest

Use {image} and {image} to evaluate f(g(5)). Select the correct answer:

Chapter 5.2 Vocab.

Time Value of Money Magic! “Active Learning Tool”

CDs and Annual Yield Lesson 25.

Compounded and Continuous Interest

Example 7 Investment The future value of $3000 invested for 3 years at rate r, compounded annually, is given by What interest rate will give a future value.

Presentation transcript:

example 2 Daily Versus Annual Compounding of Interest Chapter 5.5 a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. c.Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30. d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually?  2009 PBLPathways

a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. c.Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30. d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually?

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways a.Write the equation that gives the future value of $1000 invested for t years at 8% compounded annually. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways b.Write the equation that gives the future value of $1000 invested for t years at 8% compounded daily. Future Value of an Investment with Periodic Compounding If $P is invested for t years at the annual interest rate r, where the interest is compounded k times per year, then the interest rate per period is, the number of compounding periods is kt, and the future value that results is given by

 2009 PBLPathways c.Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30. Compounded annually Compounded daily

 2009 PBLPathways c.Graph the equations from parts (a) and (b) on the same axes with t between 0 and 30. Compounded annually Compounded daily t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S

 2009 PBLPathways Compounded annually Compounded daily d.What is the additional amount of interest earned in 30 years from compounding daily rather than annually? t S