Simple Interest

7 Key excerpts on "Simple Interest"

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  eBook - PDF

  Contemporary Mathematics for Business & Consumers

  • Robert Brechner, Geroge Bergeman(Authors)
  • 2019(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  This chapter discusses the concepts of Simple Interest; simple discount, which is a varia-tion of a Simple Interest loan; and promissory notes. Chapter 11 covers the concepts and calculations related to compound interest and present value. C OMPUTING S IMPLE I NTEREST FOR L OANS WITH T ERMS OF Y EARS OR M ONTHS Simple Interest is calculated by using a formula known as the Simple Interest formula. It is stated as follows: Interest = Principal × Rate × Time I = PRT When using the Simple Interest formula, the time factor, T , must be expressed in years or a fraction of a year. Simple Interest FormUla—YearS or monthS Years When the time period of a loan is a year or longer, use the number of years as the time factor, converting fractional parts to decimals. For example, the time factor for a 2 -year loan is 2 , 3 years is 3 , 1 1 2 years is 1.5, 4 3 4 years is 4.75, and so on. Months When the time period of a loan is for a specified number of months, express the time factor as a fraction of a year. The number of months is the numerator, and 12 months ( 1 year) is the denominator. A loan for 1 month would have a time factor of 1 12 ; a loan for 2 months would have a factor of 2 12 , or 1 6 ; a 5 -month loan would use 5 12 as the factor; a loan for 18 months would use 18 12 , or 1 1 2 , written as 1.5 . 10-1 SECTION I interest The price or rental fee charged by a lender to a borrower for the use of money. principal A sum of money, either invested or borrowed, on which interest is calculated. rate The percent that is charged or earned for the use of money per year. time Length of time, expressed in days, months, or years, of an investment or loan. Simple Interest Interest calcu-lated solely on the principal amount borrowed or invested. It is calculated only once for the entire time period of the loan. compound interest Interest calculated at regular intervals on the principal and previously earned interest.

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  eBook - PDF

  Wiley Pathways Business Math

  • Steve Slavin, Tere Stouffer(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Sim- ilarly, when you deposit money in a savings account or another savings vehicle, the bank pays you interest because it wants to give you an incentive to keep your money there. The first section in this chapter discusses Simple Interest; the second section explains compound interest, the third discusses the concept of present value, and the final section discusses basic consumer credit. 9.1 Simple Interest What is Simple Interest? Suppose you put $100 in the bank for 1 year, and the bank pays 4% Simple Interest. At the end of the year, you have $104—the $100 you started with (called the principal), and the $4 Simple Interest you earned dur- ing the year. The total amount (in this case, $104) is called the maturity value. There is another type of interest—called compound interest—that is dis- cussed later in this chapter. 9.1.1 Solving for the Unknown The formula for finding Simple Interest is or In the Simple Interest formula, ▲ Principal is the original investment or borrowed amount, represented by p. ▲ Rate (or interest rate) is the percentage charged to lend or borrow money, represented by r. ▲ Time is the length of the investment or loan, expressed in years, months, or days, represented by t. Simple Interest is the amount paid or received, calculated on the principal. Maturity value is the value of the investment after a period of time, calculated using the following formula: MV  p  I I  p  r  t Interest  Principal  Rate  Time 9.1.1 SOLVING FOR THE UNKNOWN 151 For example, how much interest is earned if $1,000 is loaned for 2 years at 6%? To figure this out, you use the following equation: As another example, how much interest is earned if $100 is invested at 8% for 6 months? (Remember to calculate 6 months as half a year, or 0.5 year.) You figure this out as follows: Use the Simple Interest formula to solve the following loan problems: 1. Paul Adams borrowed $2,000 for 1 year, at a rate of 7%.

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  eBook - ePub

  Introducing Property Valuation

  • Michael Blackledge(Author)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Part 2 Valuation mathematics

  Passage contains an image

  Compounding anddiscounting

  DOI: 10.4324/9781315680804-4

  In this chapter …

  • The difference between simple and compound interest.
  • How and why property valuation calculations use thecompound approach.
  • The basis of traditional valuation formulae and tablesand how calculators and computers can assist.
  • How allowing for interest receivable on an investmentwill affect its value today.
  • What an all risks yield is and why it is used.
  • Calculating what a sum of money invested now willaccumulate to in the future with interest added.
  • What present value is and why it is an important conceptfor property valuation.
  • Finding how much is accumulated when annual sums areinvested.

  4.1 Simple Interest

  The Oxford Dictionary of Business and Management(Law 2006 : 280) definesinterest rate as ‘the amount charged for a loan, usuallyexpressed as a percentage of the sum borrowed. Conversely, theamount paid by a bank, building society, etc. to a depositor onfunds deposited, again expressed as a percentage of the sumdeposited.’

  Interest rates are an integral function of investment. In return forthe foregoing of expenditure now, an investor can place cash intoinvestments that attract interest payments. The interest thus earnedwill hopefully offset or even surpass the reduction, due toinflation, in real value or purchasing power of the invested cashover time. Interest rates are always quoted as a percentage, and forcomparison between investments are normally referred to on an annualor ‘per annum’ basis.

  Simple Interest occurs when allinterest calculations are solely based upon the initial suminvested, referred to as the ‘principal’. The formula tocalculate the total value of an investment, at the end of aspecified time period, where Simple Interest has been earned is:

  T = P × (1 + i× n)

  Where:

  T = Terminal or final value

  P = Principal, or initial sum of money invested

  i

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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

  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 - 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

  Fundamentals of Financial Instruments

  An Introduction to Stocks, Bonds, Foreign Exchange, and Derivatives

  • Sunil K. Parameswaran(Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  That is ( 1 + rN ) < ( 1 + r ) N if N > 1 As can be seen, if Katherine were to invest for four years, Simple Interest will yield $33,000 at the end, whereas compound interest will yield $34,012.2240. Note 1: The word period used here to demonstrate the properties of simple and compound interest should be interpreted as the interest conversion period. In our illustrations, the interest was compounded once per year, so there was no ( continued ) 54 MATHEMATICS OF FINANCE ( continued ) difference between the measurement period and the conversion period; however, take the case where interest is paid at 8% per annum compounded quarterly. If so, the above properties may be stated as follows. ▪ If the investment is made for one quarter, both simple and compound interest will yield the same terminal value. ▪ If the investment is made for less than a quarter, the Simple Interest technique will yield a greater terminal value. ▪ If the investment is made for more than a quarter, the compound interest tech-nique will yield a greater terminal value. Simple Interest is usually used for short-term or current account transac-tions, that is, for investments for a period of one year or less. Consequently, Simple Interest is the norm for money market calculations. The term money market refers to the market for debt securities with a time to maturity at the time of issue of one year or less. In the case of capital market securities, however – that is, medium-to long-term debt securities and equities – we use the compound interest principle. Simple Interest is also at times used as an approximation for compound interest over fractional periods. EXAMPLE 2.7 Take the case of Alex Gunning, who deposited $25,000 with International Bank for four years and nine months. Assume that the bank pays compound interest at the rate of 8% per annum for the first four years and Simple Interest for the last nine months.

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