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ISD 151 BUSINESS MATHEMATICS

ISD 151 BUSINESS MATHEMATICS. SIMPLE INTEREST AND PROMISSORY NOTES. OUTLINE. Definition of Simple Interest Methods of Computing Simple Interest Ordinary Interest Exact Interest Computing Due Dates Promissory Notes and Discounting. SIMPLE INTEREST. Simple Interest Defined.

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ISD 151 BUSINESS MATHEMATICS

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  1. ISD 151BUSINESS MATHEMATICS SIMPLE INTEREST AND PROMISSORY NOTES

  2. OUTLINE • Definition of Simple Interest • Methods of Computing Simple Interest • Ordinary Interest • Exact Interest • Computing Due Dates • Promissory Notes and Discounting

  3. SIMPLE INTEREST

  4. Simple Interest Defined • Simple interest is the amount of money that a lender charges a borrower for credit privilege extended to him/her. • When an investor/seller/ lends money to a borrower, the borrower must pay back the money originally borrowed – called the principal and also the fee charged for the use of the money – called the interest. • This interest in usually quoted as a percentage of the principal.

  5. When part of the price is paid at the time of purchase, that part is called down payment. • If the seller or investor charges too much interest or does not extend credit, the buyer or borrower might borrow money from a third party such as a bank. • In such instances, the bank or third party will charge interest between the loan date and the repayment date. • This period of time is called the interest period or the term of the loan.

  6. The sum of the principal and the interest due is called Amount or accumulated value or maturity value. • The amount of interest is based on three factors: • The principal • The rate of Interest • The time span of the loan • The interest is quoted as an annual rate.

  7. Simple Interest Formulate Interest = Principal × Rate × Time OR I = P × R × T OR I = PRT Amount/Maturity Value = Principal + Interest

  8. Example 1 Find the Simple interest on a loan of Ȼ1,200 contracted at the rate of 6% for 4 years. What is the maturity value of this loan? Solution I = P × R × T I = 1200 × 0.06 × 4 I = Ȼ288 Maturity value (MV) = P + I = Ȼ1,200 + Ȼ288 = Ȼ1,488

  9. Example 2 Compute the interest on a credit purchase of Ȼ3,000 at 5% interest for 8 months. Solution I = PRT I = 3,000 × 0.05 × 8/12 I = Ȼ100

  10. Methods for Computing Simple Interest • Simple interest is usually computed using the exact method or the ordinary method. • The exact method uses the number of days in the year (365 days and 366 days in a leap year) in the determination of interest. • The ordinary method assumes that there are 30 days in a month and 360 days in a year. Simple Interest under this method is therefore calculated using 360 days.

  11. Computing Exact Interest • Compute the exact simple interest on a loan of Ȼ900 at 9% for 120 days. Solution I = PRT I = Ȼ900 × 0.09 × 120/365 I = Ȼ26.6301 I = Ȼ26.63

  12. Computing Ordinary Interest • Compute the ordinary simple interest on a loan of Ȼ900 at 9% for 120 days. Solution I = PRT I = Ȼ900 × 0.09 × 120/360 I = Ȼ26.73 or 27 depending on the number of decimal places used. Question: Which is better for the borrower? Exact Interest or Ordinary Interest?

  13. Given that the ordinary method uses 360 days and the Exact method uses 365 days, the denominator for the ordinary method is usually bigger and therefore interest payment under the ordinary method is higher. • The Exact interest is therefore better than the ordinary method.

  14. Calculating Due Dates • The due date of a loan is the day the amount/ maturity value of the loan is supposed to be repaid. • If the term of a loan is given in months, the due date of the loan is a corresponding day in the maturity month. • There are two conditions worth noting: • If the maturity month does not have the required number of days, then the last day of the month serves as the maturity date. • If the due date of a loan falls on a non-business day, the maturity date in either the last working day before the due date or the next working day (with additional interest charged on any additional days)

  15. Examples • A 15 – month loan dated February 2nd is due on May 2nd of the following year. • A loan dated May 31st and due in four months has a maturity date of September 30th. • A 7 – month loan dated December 4 is due on July 3 or July 5, if July 4 is a holiday. In the first two examples, the assumption is that the due dates fall on working days

  16. Calculating Time Between Calendar Days • When interest is charged in days and the method is not stated, we calculate simple interest using either the Exact or Ordinary Interest. • Under the Exact Interest, 365 days are used (t = number of days/365) whether it is a leap year or not and under the ordinary interest, 360 days are used (t = number of days/360). • There are two ways of calculating the number of days between calendar dates: • Exact time: which is the count of the actual number of days; including all except the first day. • Approximate time: assumes that each month has 30 days.

  17. Exact Time and Simple Interest • To determine simple interest using the exact time, the exact time is calculated first. We do that using the day number in the year as follows: Date Day number Dec 22 356 Mar 17 76 Exact time 280days t = 280/365 for exact simple interest and t = 280/360 for ordinary simple interest

  18. Where the period extends into the following year, the exact time is calculated as follows: • Determine exact time between September 8 and July 24. Date Day number July 24 205 + 365 for extending into the next year 570 Sep 8 - 251 Exact time 319 days and so t = 319/365 for exact simple interest and t = 319/360 for ordinary simple interest

  19. Approximate Time and Simple Interest • To determine the simple interest using approximate time, the approximate time is calculated first. • The number of days obtained is then divided by 360 days to obtain t for ordinary interest; or by 365 days to obtain t for exact interest.

  20. Example • Determine the ordinary simple interest on a loan of Ȼ5,000 contracted on December 20th at 10% given that the maturity date is March 13th ; using the approximate time method. Solution First, we determine the approximate number of days We now convert the 3 months 7 days to days by multiply the 3 by 30 and adding the 7 (i.e. 3 × 30 = 90 + 7 = 97)

  21. I = PRT I = Ȼ5,000 × 0.10 × 97/360 = Ȼ134.72 If we were determining the exact simple interest, we would have divided the 277 by 365 and I = Ȼ5,000 × 0.10 × 97/365 = Ȼ132.8

  22. Promissory Notes and Bank Discounts

  23. A promissory note is a written promise by a debtor to pay a creditor a stated sum of money on a specified date. • The debtor making the promise is called the maker of the note and the creditor is called the payee of the note. • Promissory notes are mostly used when money is borrowed or goods or services are sold on credit.

  24. Promissory notes are of two kinds: • Interest bearing • Non-interest bearing • An interest bearing promissory note is one that the maker has to pay interest at a stated rate. • A non-interest bearing promissory note does not attract any interest when it matures.

  25. Example of Promissory Note Ȼ18,700 Kumasi, November 14 2015 Three Months after date I, YaaMansah promise to pay to the order of AmiraSamed Muntaka Company Eighteen Thousand, Seven Hundred and 00/100 Cedis Value received With Interest at 26% (Exact Interest) No. 167 Due February 14, 2016 Signed

  26. Terminologies • The Face Value of the note: is the amount state in the note (Ȼ18,700) • The date of the note: is the date on which the note was made. It is from this date that interest is calculated. (November 14) • The term of the note: is the period within which the principal and the interest must be paid. (Three months)

  27. Terminologies Cont’d • The Payee of the note is the creditor to whom the promise is being made. (AmiraSamed Muntaka Company) • The maker of the note: is the person or company making the promise. (YaaMansah) • The Interest rate of the note: is the interest rate stated on the note. (26% Exact interest) • The maturity date of the note: is the date on which the amount plus interest must be honoured. (February 14, 2015)

  28. For non-interest bearing notes, value received (i.e. maturity value) is the same as the face value. • For such notes, in most cases, interest is deducted at the time money is borrowed (i.e. in advance) • An important feature of a promissory note is that it is negotiable. • Negotiable promissory notes are transferable to other persons, companies, banks, etc. by the endorsement of the payee. • Cashing a promissory note at the bank is termed as Discounting a note.

  29. Some banks usually collect interest in advance, called Bank Discount (D), which is computed on the Maturity Value (S) of the note at a specified annual discount rate (d) for the term (t) of the discount in yrs. • The term of the discount is the time (in yrs.) from the date of discount until the maturity date of the note. • If the time is given in days, the banker’s year of 360 days is used.

  30. Formula • Bank Discount (D) = Maturity value (S) × Discount rate (d) × Term of discount (t) D = Sdt • The money received for the discount note called the Proceeds (P) is obtained by deducting the Bank Discount (D) from the maturity value (S) of the note. P = S – D or P = S – Sdt P = S (1 – dt) S = P/(1 – dt)

  31. Computing Maturity Value of an Undiscounted Note • As discussed earlier, the Maturity value of a promissory note is the sum of the face value (principal) of the note and the Interest. MV = Principal + Interest Example: Compute the maturity value of an interest bearing promissory note if the face value of the note is 2000; interest is 10% exact per year; and the loan period is 60 days. Solution: I = PRT I = Ȼ2000 × 0.10 × 60/365 = Ȼ32.88 MV = Ȼ2000 + Ȼ32.88

  32. Discounting a Promissory Note • Often, when a lender holds a promissory note as security for a loan, the lender may need cash before the maturity date of the note. • One option available to the lender to get cash is to “sell” or “transfer” the note to a third party (if the note is negotiable). • If the lender transfers or sells the note, it means the third party is now assuming the risk of the loan (which is that the borrower may not repay the money on the maturity date).

  33. Therefore to acquire the note, the third party will have to earn some interest to compensate for the risk they are bearing. • This means the third party will pay the original lender less money than the maturity value of the note. • The note is then described as having been sold or transferred at a ‘discount’ and the process is termed as ‘discounting a note’

  34. Steps to Discount a Promissory Note • Compute the interest amount and the maturity value of the promissory note. • Determine the maturity (due) date of the note. • Compute the number of days in the discount period. The time (T) is the number of days in the discount period divided by 360 (or 365) or 366 days in a leap year. • Compute the discount amount (A) using the formula A = MV × R × T • Compute the proceeds by subtracting the discount amount from the maturity value.

  35. Example • On August 19, KPH Company borrows Ȼ75,000 from Mamaga Kikeli Investment Company. In return, KPH gives the company a 120-day promissory note at an ordinary simple interest rate of 8%. Compute the due date and the maturity value of the promissory note. • Mamaga Kekeli Investment Company could not wait for the note to mature and decided to transfer the note to Lakayana Financial Services on October 5 at a discount of 12% of the maturity value. Determine the discount amount and the proceeds due to Mamaga Investment Company. How much does Lakayana Financial Services make from the transaction?

  36. Solution (I) Due date = August 19 + 120 days = December 17 Interest (I) = P x R x T = Ȼ75,000 x 0.08 x 120/360 = Ȼ2,000 MV = P + I = Ȼ75,000 + Ȼ2,000 = Ȼ77,000 (II) Discount Amount = MV x Discount rate x Discount period (Time) MV = Ȼ77,000 d = 12% or 0.12 t = Oct 5 – Dec 17 = (31 – 5) + 30 + 17 = 73 days A = 77,000 x 0.12 x 73/360 = Ȼ1,873.67 Proceeds to Mamaga Company = Ȼ77,000 – Ȼ1,873.67 = Ȼ75,126.33 Lakayana will pay Mamage company Ȼ75,126.33 for the note Lakayana earned Ȼ77,000 - Ȼ75,126.33 = Ȼ1,873.67

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