Chapter 1 – Simple Interest and Bank Discount.pdf

Chapter 1 – Simple Interest and Bank Discount After you read this chapter, you should be able to:  Discuss the difference between lender or creditor and barrower or debtor  Understand how to compute maturity date  Discuss the concept of time  Discuss how to calculate Bank discount and Promi...

Chapter 1 – Simple Interest and Bank Discount After you read this chapter, you should be able to:  Discuss the difference between lender or creditor and barrower or debtor  Understand how to compute maturity date  Discuss the concept of time  Discuss how to calculate Bank discount and Promissory note Core Values “For I know the plans I have for you, declares the LORD, plans for welfare and not for evil, to give you a future and a hope.” - Jeremiah 29:11 Learning Activities and resources  Valuation, Methods and models applied in corporate finance by George Chacko and Carolyn L. Evans  Investment Mathematics by WIN Ballada, CPA, CBE, MBA and Susan Ballada, CPA, 2015 issue 4th Edition  Fundamentals of Financial Management (with industry based perspective) by Ma. Flordeliza Anastacio Ph. D, Robert Dacanay and Leonardo Aliling, Rex Bookstore, 2014  Financial Management: An Introduction by Scott Smart and William Megginson, Cengage Learning, 2009  Business Finance Second Edition by Roberto G. Medina, Ph. D. Rex Bookstore, 2011 Introduction “Money makes money, and the money that money makes, makes more money” - Benjamin Franklin SIMPLE INTEREST Individuals, whether engaged in business or not, occasionally find themselves in need of funds for worthwhile purposes. One recourse they usually resort to is borrowing. On the other hand, a business or person who has excess money may want to invest this through lending. The one who invests the money is the lender or creditor and the one who owes it, is the borrower or debtor. The lender, of course, expects a sum in addition to what he has lent; this is actually the interest—the income he has earned. However, on the part of the borrower, this interest is his, cost for the use of money. Simply stated) interest is money paid for the use of money. Interest may be computed by either of the two most common methods—simple or compound. Simple interest is an interest computed on the amount the borrower received at the time the loan is obtained and is added to that amount when the loan becomes due. Thus, simple interest is computed only once for the entire time period of the loan. At the end of the time period, the borrower repays the amount originally owed plus the interest. Some lenders, however, prefer to collect the interest in advance. The interest deducted in advance is called bank discount. This is discussed in another section of this chapter. Simple interests are usually applied to loans whose time period is less than a year. Compound interest, on the other 'hand, means that the interest is computed more than once during the time period of the loan. Compound interest loans are generally for time periods of a year or longer. This will be discussed in detail in Chapter 2 of this book. The computation of simple interest considers three factors: principal, rate and time. In this section, simple interest rate is referred to as interest rate or rate and simple interest as interest. Illustration: Luz Clarita borrowed P280,000 at a simple interest rate of 9% for one year. Compute for the simple interest and maturity value of the loan. Finding the simple interest Simple interest is the product of the principal, rate and time; or stated as a formula, Interest = Principal x Rate x Time The principal is the amount of deposit made by a depositor or the face amount lent to the borrower on loan date. In the illustration, the principal is P280,000. The simple interest rate expressed as a percentage, is converted to a decimal for computation purposes. Unless otherwise stated, the simple interest rate is an annual rate, In the illustration, the rate is 9% or in decimal form,.09. The time is the length of time for which the money is- borrowed or lent. The time expressed in years or fractional part of a year is the period between the loan date—the date when the loan was obtained and maturity date—the date when the loan becomes due. In the illustration, the time is one year. The simple interest may now be computed using the formula I=PRT. Substituting the givens in the illustration, I = PRT I = 280,000 x.09 x 1 I = P25,200 Thus, a loan of P280,000 for one year at simple interest rate of 9% will cost Luz Clarita P25,200 in interest. Finding the maturity value After one year, Luz Clarita's loan matures, and she is obliged to pay the maturity value of the loan. This is the sum of the principal she received on loan date and the interest. In formula, Maturity Value = Principal + Interest The maturity value is solved as, Maturity Value = Principal + Interest Maturity Value = 280,000 + 25,200 Maturity Value = P305,200 Hence, on maturity date, in addition to the principal of P280,000 that Luz Clarita received when she obtained the loan, she is to pay P25,200 in interest; or a total of P305,200. The Concept of Time The time T in the simple interest formula I = PRT is the period between the loan date and the maturity date. In the previous illustration, time is exactly one year. With the simple interest rate expressed as an annual rate and with the time expressed in Years' the computation of interest and maturity value in the illustration is as simple as just getting the product of the principal, rate and time. If the time in years is not exact, say, 1 year and six months or 1 ½ years, it has to be converted to decimal hence it becomes 1.5 years; 2 years and 3 months or 2 ¼ years becomes 2.25 years; and 3 years and 9 months or 3 ¾ years becomes 3.75 years. This, of course, is being done to facilitate the computation. In other cases, the time T may be given in months. Be it more than 12 months or less, the 12-month period is used in converting time into a fractional form. Again, since the simple interest rate is given as an annual rate, the time should be prorated accordingly. It is also advisable to convert the time in months to decimal form. By doing this, the time in months is actually converted in terms of years. For example, the time of 9 months or 9/12 is.75 year; 15 months or 15/12 is 1.25 years; and 30 months or 30/12 is 2.5 years. However, in instances when it would be impracticable to convert the number of months to decimal form, say, 7 months or 7/12, the fractional form may be substituted to the simple interest formula as is. If the time T is given in months and only the loan date is stated, the maturity date shall coincide with the loan date. Thus, a loan obtained on June 13, 2012 payable in 4 months will mature Oct. 13, 2012. In addition, if either the loan date or maturity date does not make mention of the year, it shall be assumed that these dates fall on the same year. For example, a loan that was granted on Feb. 14, 2012 and to mature Sept. 20 would mature on sept. 20, 2012. There are also cases when the time T is stated as a certain number of days. It follows that the year should likewise be measured in terms of the number of days. Two methods are at hand: first, the exact interest method, which uses 365 days as the time denominator; and second, the ordinary interest method, which uses 360 days. Note that the exact interest method uses 366 days in a leap year. Illustration: If Esperanza borrowed P 140,000 at 7% interest for 64 days, how much would the interest be using the exact and ordinary interest methods? Note that the ordinary interest method yielded a higher interest. When only the loan date and maturity date are given, the number of days may be counted as either actual time or approximate time. Actual time is determined by counting every day excluding the loan date until the maturity date while approximate time by assuming that each month has 30 days. illustration: Count the actual time and approximate time from April 8, 2012 to Sept. 20, 2012. It turns out that actual time is longer than approximate time. But note that what have been counted so far is the time numerator. The next problem is which time denominator to use. This, as discussed, uses either the exact interest method using the 365-day period, r the ordinary interest method using the 360-day period. It may be deduced from the above discussions that where only the loan date and maturity date are given, there are four possible time combinations. Applying this in our illustration, Illustration: Applying the four time combinations above, compute for the interest if Esperanza was lent P 122,500 at 11% interest. 1. Exact interest using actual time 3. Ordinary interest using actual time Interest = Principal x Rate x Time Interest = Principal x Rate x Time Interest = 122,500 x.11 x 165/365 Interest = 122,500 x.11 x 165/360 Interest = P6,091.44 Interest = P6,176.04 2. Exact interest using approximate time 4. Ordinary interest using approximate time Interest = Principal x Rate x Time Interest = Principal x Rate x Time Interest = 122,500 x.11 x 162/365 Interest = 122,500 x.11 x 162/360 Interest = P5,980.68 Interest = P6,063.75 Esperanza must have realized that ordinary interest using actual time is most favorable to her since it yielded the highest interest. This time combination also known as the Banker's Rule is being adopted by banks. For problem solving purposes, this shall be used whenever the problem is silent as to which time combination to use. Review Questions! 1. What are the two most common methods businesses use in computing interest? 2. What are the factors being considered in computing for the simple interest? State the simple interest formula. 3. Enumerate the four time combinations. Which among these is referred to as the Banker’s rule? 4. Find the simple interest on P8,000 loaned at an annual interest rate of 12% for two years. 5. What is the maturity value of the loan in the previous problem? 6. Find the time, in days, of each of the following notes using Actual time and Approximate time: a. January 10, 2021 to May 18, 2021.