1. An account with a balance of $1000 pays 3. 65% annual

Slides:

Advertisements

Similar presentations

EXAMPLE 5 Model continuously compounded interest A = Pe rt SOLUTION Finance You deposit $4000 in an account that pays 6% annual interest compounded continuously.

Advertisements

EXAMPLE 1 Multiplying Decimals decimal places + 2 decimal places 4 decimal places.

EXAMPLE 5 Find the balance in an account You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest.

Copyright © 2008 Pearson Education, Inc. Slide 4-1 Unit 4B The Power of Compounding.

Section 4.1 Logarithms and their Properties. Suppose you have $100 in an account paying 5% compounded annually. –Create an equation for the balance B.

6-7 Change each percent to a decimal. 1.4% 2.9%3.2.0% 4.6.5% % % COURSE 2 LESSON 9-7 (For help, go to Lessons 6-2.) Simple and Compound Interest.

The Number e and Natural Logs Chapter 8.4 and 8.3.

7.4a Notes – Evaluate Logarithms. 1. Solve for x. a. x = 2 b. c.d. x = 1 x = 0 x = -2.

Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.

THE NATURAL BASE EXAMPLE 1 Simplify natural base expressions Simplify the expression. a.e2e2 e5e5 = e = e7e7 b. 12e4e4 3e3e3 = e 4 – 3 4 = 4e4e.

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

Notes Over 7.1 no real 4th roots Finding nth Roots

Section 4A The Power of Compounding Pages

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

The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.

Section 5-4 The Number e and the Function. The number e You have already seen many exponential functions. In advanced mathematics, the most important.

6.6 The Natural Base, e Warm-up Learning Objective: To evaluate natural exponential and natural logarithmic functions and to model exponential growth and.

Math – Solving Problems Involving Interest 1.

Simple and Compound Interest Video: Simple/ Compound InterestSimple/ Compound Interest Video: A Penny a DayA Penny a Day.

EXAMPLE 1 Find nth roots Find the indicated real nth root(s) of a.

Pre-Algebra Simple and Compound Interest Suppose you deposit $1,000 in a savings account that earns 6% in interest per year. Lesson 7-8 a. Find the interest.

Exponent Quiz Review. Evaluate the expression 4 2  Answer: 16.

Converting a Decimal to Scientific Notation 1. Count the number N of places that the decimal point must be moved in order to arrive at a number x, where.

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

Compound Interest Making Money!!!. Compound Interest Solving by Hand A=P(1+r/n) nt P - Initial principal r – annual rate expressed as a decimal n – compounded.

4.3 Use Functions Involving e PROJECT DUE: Tomorrow Quiz: Tomorrow Performance Exam: Friday *We will be having a book check tomorrow…. BRING BOTH.

Objectives: 1. Be able to find the Euler Number. 2.Be simplify expressions using the Natural base (with a calculator also) 3.Be able to graph a Natural.

ObjectiveDOL  SWBAT solve and create exponential equations using logs.  (CCSS: A-CED.2)  2.4.a.ii  (CCSS: A-CED.1)  2.4.a.i  Given 2 multiple.

3-5 COMPOUND INTEREST FORMULA

Simplify the expression.

Compound Interest Making Money!!!.

Exponential Functions and Their Graphs (Day 2) 3.1

4.2 Exponential Functions

EXAMPLE 5 Find the balance in an account

1. Credit and borrowing Cambridge University Press  G K Powers 2013

CHAPTER 8 Personal Finance.

Compound Interest.

8.3 Compound Interest HW: (1-21 Odds, Odds)

(10 ) WARM UP Simplify the expression. 1. e –4x e12x ANSWER

Lesson 6.2 The Natural Base e

04 Evaluate nth Roots and Use Rational Exponents

Applications of Exponential Functions

Compound Interest I.. Compound Interest: A = P ( 1 + r/n)nt

Compound Interest Making Money!!!.

3-8 PRESENT VALUE OF INVESTMENTS

7.3 Use Functions Involving e

Exponential Functions

Exponential Functions

Chapter 5: Exponential and Logarithmic Functions

Savings and Interest Lesson 4.4.

1. Find the inverse of the function y = 3x – 5.

Chapter 10.5 Base e and Natural Logarithms Standard & Honors

2-4 Explore Compound Interest

Day 86 – Introduce the power of interest

Objective The student will be able to:

Savings and Interest Skill 11.

Simple and Compound Interest Formulas and Problems

CHAPTER 8 Personal Finance.

5.1 nth Roots and Rational Exponents

Writing and applying exponential functions

25 = 32 Properties of Exponents Exponent Exponential Form Decimal Form

Notes Over 8.3 Simplifying Natural Base Expressions

Work out (if you can, simplify your answer) 8 6.

Click the mouse button or press the Space Bar to display the answers.

Compounded and Continuous Interest

3-6 Continuous Compounding

8.3 The Number e.

§8.3, Compound Interest.

Presentation transcript:

1. An account with a balance of $1000 pays 3. 65% annual 1. An account with a balance of $1000 pays 3.65% annual interest compounded daily. What is the balance at the end of 1 year if no money is added to the principal? ANSWER $1037.17 Think: What if this interest was compounded.. Every hour? Every minute? Every second? Continuously?

EXAMPLE 1 Leonhard Euler (1707-1783) Natural base “e”

(5 ) ( ) EXAMPLE 1 Simplify natural base expressions Simplify the expression. a. e2 e5 = e2 + 5 = e7 b. 12 e4 3 e3 = e4 – 3 4 = 4e (5 ) c. e –3x 2 = 52 ( e –3x ) 2 = 25 e –6x = 25 e6x

EXAMPLE 2 Evaluate natural base expressions Use a calculator to evaluate the expression. Expression Keystrokes Display a. e4 [ ] ex 4 54.59815003 b. e –0.09 [ ] ex 0.09 0.9139311853

GUIDED PRACTICE for Examples 1 and 2 Simplify the expression. 1. e7 e4 e11 ANSWER 2. 2 e–3 6e5 12 e2 ANSWER 3. 24 e8 4 e5 6 e3 ANSWER

GUIDED PRACTICE 4. Simplify (ex e –3x)2. 1 e4x ANSWER 5. Use a calculator to evaluate e –0.35. (Round to three decimal places.) ANSWER 0.705