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Pre-Calculus

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Rational Functions

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Modeling with Rational Functions

Learn How Your Money Doubles with Compound Interest!

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Learn How Your Money Doubles with Compound Interest!
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Chelsea

@zuncho

·

625 Followers

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A comprehensive guide to calculate doubling time for compound interest and understanding interest rate calculations.

• Compound interest calculations involve different methods including simple interest, periodic compounding, and continuous compounding
• Understanding the relationship between effective interest rate vs nominal rate calculation is crucial for accurate financial planning
• The guide provides detailed examples of continuous compounding investment example scenarios
• Mathematical formulas are presented for calculating doubling time, effective rates, and required deposits
• Real-world applications include scenarios for saving for down payments and investment growth calculations

2/22/2023

111

5.6 Notes COMPOUND INTEREST Objectives: 1) Find the amount of time it takes to double an investment. FORMULAS SIMPLE INTEREST (ANNUAL) A = P

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Page 2: Advanced Applications and Problem Solving

This page demonstrates practical applications through various financial scenarios and calculations involving compound interest.

Example: A $15,000 down payment goal calculation shows:

  • Monthly compounding requires $12,285.05 initial deposit
  • Continuous compounding requires $12,220.97 initial deposit

Highlight: When converting between nominal and effective rates with continuous compounding:

  • A 6% nominal rate yields approximately 6.18% effective rate
  • A 6% effective rate requires approximately 5.83% nominal rate

Definition: The relationship between nominal and effective rates demonstrates how compounding frequency affects actual returns on investments.

5.6 Notes COMPOUND INTEREST Objectives: 1) Find the amount of time it takes to double an investment. FORMULAS SIMPLE INTEREST (ANNUAL) A = P

View

Page 1: Understanding Compound Interest Fundamentals

This page introduces the core concepts of compound interest calculations and their practical applications. The content focuses on different compounding methods and their comparative outcomes.

Definition: Compound interest is interest calculated on both the initial principal and accumulated interest from previous periods.

Vocabulary:

  • Nominal Rate: The stated interest rate before considering compounding effects
  • Periodic Rate: The interest rate applied in each compounding period
  • Effective Rate (APR): The equivalent simple interest rate that yields the same final amount as compound interest

Example: A $12,000 deposit compared across quarterly and continuous compounding with 9% annual interest rate:

  • Quarterly compounding yields $18,726.11
  • Continuous compounding yields $18,819.74

Highlight: The doubling time formula for continuous compounding is T₂ = (ln 2)/r, which for a 9% rate equals approximately 7.7 years.

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Know Exponential Functions thumbnail

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Exponential Functions

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the # 1 ranked education app in five European countries

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Students use Knowunity

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In Education App Charts in 12 Countries

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

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SuSSan, iOS User

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Subjects

/

Pre-Calculus

/

Rational Functions

/

Modeling with Rational Functions

Learn How Your Money Doubles with Compound Interest!

user profile picture

Chelsea

@zuncho

·

625 Followers

Follow

A comprehensive guide to calculate doubling time for compound interest and understanding interest rate calculations.

• Compound interest calculations involve different methods including simple interest, periodic compounding, and continuous compounding
• Understanding the relationship between effective interest rate vs nominal rate calculation is crucial for accurate financial planning
• The guide provides detailed examples of continuous compounding investment example scenarios
• Mathematical formulas are presented for calculating doubling time, effective rates, and required deposits
• Real-world applications include scenarios for saving for down payments and investment growth calculations

2/22/2023

111

 

Pre-Calculus

6

5.6 Notes COMPOUND INTEREST Objectives: 1) Find the amount of time it takes to double an investment. FORMULAS SIMPLE INTEREST (ANNUAL) A = P

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Access to all documents

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Join milions of students

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Page 2: Advanced Applications and Problem Solving

This page demonstrates practical applications through various financial scenarios and calculations involving compound interest.

Example: A $15,000 down payment goal calculation shows:

  • Monthly compounding requires $12,285.05 initial deposit
  • Continuous compounding requires $12,220.97 initial deposit

Highlight: When converting between nominal and effective rates with continuous compounding:

  • A 6% nominal rate yields approximately 6.18% effective rate
  • A 6% effective rate requires approximately 5.83% nominal rate

Definition: The relationship between nominal and effective rates demonstrates how compounding frequency affects actual returns on investments.

5.6 Notes COMPOUND INTEREST Objectives: 1) Find the amount of time it takes to double an investment. FORMULAS SIMPLE INTEREST (ANNUAL) A = P

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Understanding Compound Interest Fundamentals

This page introduces the core concepts of compound interest calculations and their practical applications. The content focuses on different compounding methods and their comparative outcomes.

Definition: Compound interest is interest calculated on both the initial principal and accumulated interest from previous periods.

Vocabulary:

  • Nominal Rate: The stated interest rate before considering compounding effects
  • Periodic Rate: The interest rate applied in each compounding period
  • Effective Rate (APR): The equivalent simple interest rate that yields the same final amount as compound interest

Example: A $12,000 deposit compared across quarterly and continuous compounding with 9% annual interest rate:

  • Quarterly compounding yields $18,726.11
  • Continuous compounding yields $18,819.74

Highlight: The doubling time formula for continuous compounding is T₂ = (ln 2)/r, which for a 9% rate equals approximately 7.7 years.

Similar Content

Pre-Calculus - Exponential Functions

Exponential growth and decay word problems and formulas.

19

347

0

Know Exponential Functions thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying