Interest

7 Key excerpts on "Interest"

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  eBook - ePub

  An Undergraduate Introduction to Financial Mathematics

  • J Robert Buchanan(Author)
  • 2012(Publication Date)
  • WSPC

    (Publisher)

  Chapter 1 The Theory of Interest One of the first types of investments that people learn about is some variation on the savings account. In exchange for the temporary use of an investor's money, a bank or other financial institution agrees to pay Interest, a percentage of the amount invested, to the investor. There are many different schemes for paying Interest. In this chapter we will describe some of the most common types of Interest and contrast their differences. Along the way the reader will have the opportunity to renew their acquaintanceship with exponential functions and the geometric series. Since an amount of capital can be invested and earn Interest and thus numerically increase in value in the future, the concept of present value will be introduced. Present value provides a way of comparing values of investments made at different times in the past, present, and future. As an application of present value, several examples of saving for retirement and calculation of mortgages will be presented. Sometimes investments pay the investor varying amounts of money which change over time. The concept of rate of return can be used to convert these payments in effective Interest rates, making comparison of investments easier. 1.1 Simple Interest In exchange for the use of a depositor's money, banks pay a fraction of the account balance back to the depositor. This fractional payment is known as Interest. The money a bank uses to pay Interest is generated by investments and loans that the bank makes with the depositor's money. Interest is paid in many cases at specified times of the year, but nearly always the fraction of the deposited amount used to calculate the Interest is called the Interest rate and is expressed as a percentage paid per year. For example, a credit union may pay 6% annually on savings accounts

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  eBook - ePub

  Finite Mathematics

  Models and Applications

  • Carla C. Morris, Robert M. Stark(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Chapter 2 Mathematics of Finance

  1. 2.1 Simple and Compound Interest
     1. Simple Interest
        1. Example 2.1.1 Simple Interest
        2. Example 2.1.2 A Savings Account
     2. Compound Interest
        1. Example 2.1.3 Compound Interest
        2. Example 2.1.4 Effects of Compounding Periods
        3. Example 2.1.5 Compounding Continuously
     3. Effective Rate of Interest
        1. Example 2.1.6 Effective Rate of Interest
        2. Example 2.1.7 Annual Percentage Rate
     4. Present Worth
        1. Example 2.1.8 Present Worth
        2. Example 2.1.9 Real Estate Bargains
  2. 2.2 Ordinary Annuity
     1. 1. Example 2.2.1 Future Value Calculation
        2. Example 2.2.2 An Annuity Accumulation
        3. Example 2.2.3 An Annuity Payout
        4. Example 2.2.4 Present Value of an Annuity
  3. 2.3 Amortization
     1. 1. Example 2.3.1 Amortization Schedule
        2. Example 2.3.2 Amortization
        3. Example 2.3.3 Mortgage Payment
  4. 2.4 Arithmetic and Geometric Sequences
     1. 1. Example 2.4.1 Arithmetic Sum
        2. Example 2.4.2 Geometric Series
        3. Example 2.4.3 Compound Interest
        4. Example 2.4.4 Benjamin Franklin's Bequest
     2. Fibonacci Numbers
        1. Example 2.4.5 Fibonacci Sequence
  5. Historical Notes

  2.1 Simple and Compound Interest

  Simple Interest

  You have heard the refrain: “A dollar today is not the same as a dollar tomorrow.” Used in many contexts, here we mean that money earns more money!

  Interest is monies paid or received for the use of money. When you borrow money, your promise to pay Interest is the inducement for lenders to part with their money. In your savings or money market accounts, you are the lender, and your accounts are credited with Interest.

  The money borrowed is the principal. The Interest rate

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  eBook - ePub

  Foundations and Applications of the Time Value of Money

  • Pamela Peterson Drake, Frank J. Fabozzi(Authors)
  • 2009(Publication Date)
  • Wiley

    (Publisher)

  In the case of compound Interest, the amount repaid has three components:1. The amount borrowed 2. The Interest on the amount borrowed 3. The Interest on Interest

  The basic valuation equation is the foundation of all the financial mathematics that involves compounding, and if you understand this equation, you understand most everything in financial mathematics: where: FV = the future value PV = the present value i = the rate of Interest n = is the number of compounding periods

  FV = PV(1 + i )

  n

   

  The term (1 + i)

  n

  is the compound factor. When you multiply the value today—the present value—by the compound factor, you get the future value.

  We can rearrange the basic valuation equation to solve for the present value, PV: where 1 ÷ (1 + i)

  n

  is the discount factor. When you multiply the value in the future by the discount factor, you get the present value.

  In sum, The focus of this chapter is on compounding—that is, determining a value in the future. We look at discounting in the next chapter.

  OF Interest

  The word Interest is from the Latin word intereo, which means “to be lost.” Interest developed from the concept that lending goods or money results in a loss to the lender because he or she did not have the use of the goods or money that is loaned.

  In the English language, the word usury is associated with lending at excessive or illegal Interest rates. In earlier times, however, usury (from the Latin usura, meaning “to use”) was the price paid for the use of money or goods.

  COMPOUNDING

  We begin with compounding because this is the most straightforward way of demonstrating the effects of compound Interest. Consider the following example: You invest $1,000 in an account today that pays 6% Interest, compounded annually. How much will you have in the account at the end of one year if you make no withdrawals? Using the subscript to indicate the year the future value is associated with, after one year you will have

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  eBook - PDF

  Pocket Book of Integrals and Mathematical Formulas

  • Ronald J. Tallarida(Author)
  • 2015(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  189 12 Financial Mathematics 12.1 Simple Interest An item or service costs an amount C and is to be paid off over time in equal installment payments. The difference between the cost C and the total amount paid in installments is the Interest I . The Interest rate r is the amount of Interest divided by the cost and the time of the loan T (usually expressed in years): r = I / CT Example An item purchased and costing $4,000 is to be paid off in 18 equal monthly payments of $249. The total amount paid is 18 × $249 = $4,482, so that I = $482. The time of the loan is 1.5 years; hence, the rate is r = 482/(4000 × 1.5) = 0.0803 or 8.03%. 190 Integrals and Mathematical Formulas Note: While the above computation is correct, the computed rate, 8.03%, is misleading. This would be the true rate only if the $4,482 were repaid in one payment at the end of 18 months. But since you are reducing the unpaid balance with each payment, you are paying a rate higher than 8.03%. True Interest rates are figured on the unpaid balance. The monthly payment based on the true rate is discussed below. 12.2 True Interest Formula (Loan Payments) The Interest rate is usually expressed per year; thus, the monthly rate r is 1/12th of the annual Interest rate. The monthly payment P is computed from the amount borrowed, A , and the number of monthly payments, n , according to the formula P Ar r r r n n = + + -> ( ) ( ) ( ) 1 1 1 0 Example A mortgage of $80,000 ( A ) is to be paid over 20 years (240 months) at a rate of 9% per year. The monthly payment is computed from the above formula with n = 240 months and r = 0.09/12 = 0.0075 per month. It is necessary to calculate (1 + 0.0075) 240 for use in the formula. This is accomplished with 191 Financial Mathematics the calculator key [ y x ]; that is, enter 1.0075, press the [ y x ] key, then 240 = to give 6.00915. The above formula yields P = × × -= 80000 0 0075 6 00915 6 00915 1 719 78 .

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  eBook - PDF

  Financial Rules for New College Grads

  Invest before Paying Off Debt—and Other Tips Your Professors Didn't Teach You

  • Michael C. Taylor(Author)
  • 2018(Publication Date)
  • Praeger

    (Publisher)

  If you find math terrifying, you have my permission to skip ahead 16 The Financial Rules for New College Graduates to Chapters 6 through 21. Just promise me you’ll eventually come back to the beginning? Chapters 6 through 21 are greatly enhanced by an understanding of inter- est rates from this chapter and the math of Chapters 4 and 5. My justification for claiming that this book will make you money is built largely on an under- standing of Interest rates, compound Interest, and discounted cash flows, the subjects of Chapters 3, 4, and 5. The reasons I’ve placed the math in this book upfront—knowing it will turn off some readers—are that I feel extremely passionately that: 1. These are key finance tools everyone should have. 2. They are absolutely in reach of a reader like you. 3. Using these math tools will make a lifetime of good financial choices so much more likely. You won’t need to depend on financial gurus to justify choices for you. You can work out the justification for yourself using the astonishing precision of mathematical truth. OK, that’s it for the moment on parenthetical book-structure notes. Let’s get back to . . . Interest Rates in Practice Let’s start with the basic mechanics of Interest rates, before moving on to the theoretical and metaphorical. If I lend my $100 to my neighbor Bob for a year at a 6% annual Interest rate, the stated Interest rate means that I will receive $6 back from Bob at the end of the year, in addition to my original $100, because $6 is 6% of the origi- nal $100. Conversely, if I borrow $100 from Nina and agree to pay an 8% annual Interest rate on the loan, I will owe Nina both the $100 back as well as $8, for a total of $108 at the end of 1 year. Borrowing and lending money generally involves charging a percentage of the original amount as Interest, which compensates the lender by returning a larger amount of money to him or her in the future.

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  eBook - ePub

  Money and Banking

  An International Text

  • Robert Eyler(Author)
  • 2009(Publication Date)
  • Routledge

    (Publisher)

  2 Interest rates and financial markets

  Introduction

  Interest rates represent prices of every economic action because they represent both opportunity costs for the use of goods, services and inputs and connect time periods to each other. The sacrifice of consumption today must come with a reward, and consuming today must have its cost. There are many Interest rates, one for every asset that exists. The “price” of an asset is in part determined by an Interest rate. Interest rates are used in business plans to discount the future, as income to those who have deposited money, purchased stocks and bonds, and to those who make a loan. It is a cost to those who borrow, the cost of consuming more than you can afford at a given time. It is also the cost of not buying something that could produce income. We can summarize the Interest rate’s definition generally in four ways:

  • The revenue from lending or not consuming; • The cost of borrowing or consuming; • The opportunity cost of holding money as cash; and • A measure of time preference concerning consumption.

  Interest rates come in many forms, all with the same basic set-up. An Interest rate includes measures of risk, both general and very specific. When you borrow money, the rate at which you borrow is the nominal rate. This rate is the stated Interest cost or return of a financial investment. There is also a real rate, but what separates the two? The difference between nominal and real variables in economics has to do initially with inflation, or purchasing power erosion, and other risks. In its most basic form, a nominal Interest rate has the following equation:

  R = r + P

  (2.1)

  where R is a nominal rate, r is the associated real rate and P

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  eBook - PDF

  Understanding the Mathematics of Personal Finance

  An Introduction to Financial Literacy

  • Lawrence N. Dworsky(Author)
  • 2009(Publication Date)
  • Wiley

    (Publisher)

  The formula is Interest Principal Rate Time = ( )( )( ). Time must be expressed in the same units as rate. In other words, if the rate is expressed in percentage per year, then the time must also be expressed in years. If the rate is in percentage per month, then the time must be in months. The Interest calculated, of course, is for the time period that the rate is expressed in. The same example as above would therefore be written as Interest = ( )( )( ) = $ , . . . $ . . 1 200 00 0 06 1 0 72 00 The following are a few more examples: The simple Interest on an $800 loan with an Interest rate of 8% per year after 2 years is Interest = ( )( )( ) = $ . . $ . . 800 00 0 08 2 128 00 Chapter 2 Compound Interest 27 The simple Interest on a $2,500 loan with an Interest rate of 5% per year after 18 months is (remember that 18 months is 1.5 years) Interest = ( )( )( ) = $ , . . . $ . . 2 500 00 0 05 1 5 187 50 As I have stated above, simple Interest is rarely used in real transactions. For that matter, the term Interest when used alone does not mean simple Interest. It means compound Interest. In a compound Interest loan, there is a period of time called the compounding interval or the compounding period. Suppose you are told that your loan will be compounded monthly, starting 1 month after you originate the loan. Starting 1 month after you originate the loan, and monthly thereafter, Interest is calculated on the total amount of money that you owe. This is very different from simple Interest in that the Interest from each compounding calculation is added to the amount of money you owe, now called your balance, and subsequent Interest calculations are calcu- lated based on this balance. I need to introduce one other convention before presenting some Interest calcu- lation examples. It is conventional to present the terms of a loan as the annual Interest rate and the compounding intervals.

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