Continuously Compounded Interest. A Limit Involving e Numerically evaluate the following limit: x 101001000 10000 100000 1000000 10000000 f(x)f(x) 2.5942.7052.7172.718.

Slides:

Advertisements

Similar presentations

Lesson 4-4 Example Example 1 1.Change each decimal to a fraction. Order, 0.5,, and –0.8 from least to greatest. Graph the numbers on a number line.

Advertisements

L’Hôpital’s Rule. Another Look at Limits Analytically evaluate the following limit: This limit must exist because after direct substitution you obtain.

Multiplying Decimals 1. Multiply 2. Move the decimal.

L’Hôpital’s Rule.

Compound Interest.

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 Compound Interest? Compound interest is interest that is compounded at certain intervals or earned continuously (all the time). Annually: A = P(1.

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.

11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.

3-3 Example 1 Find the simple interest earned on an investment of $500 at 7.5% for 6 months. 1. Write the simple interest formula. I = prt Lesson 3-3 Example.

Rational Numbers and Decimals

7-6 & 7-7 Exponential Functions

7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.

The Number e and Natural Logs Chapter 8.4 and 8.3.

WARM UP 4 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙

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.

Solving Inequalities Solving Inequalities Objective: SWBAT solve and graph compound inequalities.

Chapter 10 L10-6 Notes: Percents to Decimals. Percent to Decimal To write a percent as a decimal, rewrite the percent as a fraction with a denominator.

Aim: How do we solve exponential equations using common or natural logarithms? Do Now: 1. Solve for x: 3 x = Solve for x: 4 x = 8 3. Solve for x:

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

Adding and Subtracting Unlike Fractions Lesson 4-3.

Fractions and Decimals. Writing Decimals as Fractions Use the decimal as the numerator. Use the place value as the denominator (for example, if the decimal.

Notes Over 3.5Interest Simple interest is found by multiplying the principal, the rate, and the time. Compound interest is the total amount earned each.

Simple Interest Formula I = PRT. I = interest earned (amount of money the bank pays you) P = Principle amount invested or borrowed. R = Interest Rate.

Indeterminate Forms and L’Hopital’s Rule Chapter 4.4 April 12, 2007.

Renaming Fractions as Decimals The trick to this is to get the fraction in a base divisible by The denominator is in base 10. The zeros in the.

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

Decimal Operations Objective: To solve decimal problems correctly by using the correct place values.

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.

Integration by Substitution (4.5) February 7th, 2013.

EXAMPLE 2 Multiply by the LCD Solve. Check your solution. x – 2 x = SOLUTION x – 2 x = Multiply by LCD, 5(x – 2). 5(x – 2) x – 2 x 1 5.

February 9, 2012 At the end of today, you will be able to solve exponential functions. Warm-up: Evaluate without a calculator 1.arcsin HW 3.1b:

Future Value of Investments

Section 11.3 – The Number e. Compound Interest (Periodically) A – Accumulated Money P – Principal (Initial Amount) r – Interest Rate (in decimal form)

COMPOUND INTEREST Objective: You will be able to apply the formula for compound interest to a given problem or word problem.

Section 8-2 Properties of Exponential Functions. Asymptote Is a line that a graph approaches as x or y increases in absolute value.

Compound Interest. Compound Interest (except continuous) When the bank pays interest on both the principal and the interest an account has already earned,

Let’s COUNT In tenths

8.9: Finding Power Series Using Algebra or Calculus Many times a function does not have a simple way to rewrite as the sum of an infinite geometric series.

Exercise Write 5% as a decimal Write 6.5% as a decimal Exercise.

1. Multiply 2. Move the decimal

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

Exponential Functions and Their Graphs (Day 2) 3.1

Chapter 9 Review.

Adding and Subtracting Unlike Fractions

Adding and Subtracting Unlike Fractions

Compound Interest.

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

Before we look at 7-2… A few more examples from 7-1.

Chapter 3: Consumer Math

Learning Journey – Percentages

SIMPLE AND COMPOUND INTEREST

Savings and Interest Lesson 4.4.

Find the sum of , if it exists.

Section 5.1 – Exponential Functions

Representation of Functions by Power Series (9.9)

Subtracting Like and Unlike Fractions

2-6 Continuous Compounding

Savings and Interest Skill 11.

2-7 Future Value of Investments

Subtracting Like and Unlike Fractions

Chapter 5.2 Vocab.

equivalent expression

Compounded and Continuous Interest

Compound Interest.

Do Now 1/22/19 Take out HW from last week. Copy HW in your planner.

6.1 Applications of Exp. Functions & 6.2 The Natural Exp. Function

Presentation transcript:

Continuously Compounded Interest

A Limit Involving e Numerically evaluate the following limit: x f(x)f(x)

Compound Interest P = Principal Amount (original) r = decimal rate ( % ÷ 100 ) t = time in years n = number of intervals

A Limit Involving Compound Interest Analytically evaluate the following limit: Rewrite the limit so it resembles the limit involving e. Let x = n/r. This limit represents interest that is compounded infinitely many times a year (continuous).

Continuously Compounded Interest P = Principal Amount (original) r = decimal rate ( % ÷ 100 ) t = time in years