REV 00 CHAPTER 8 PROMISSORY NOTE QMT 3301 BUSINESS MATHEMATICS 1 REV 00 8.1 Promissory Note A written document made by one person or party to pay a stated sum of money on a specified future date to another person or party. Are negotiable documents and can be of two types; interest bearing notes and noninterest bearing notes. The main features of a promissory note are as follows: QMT 3301 BUSINESS MATHEMATICS 2 1. Maker The maker is the person that signs the note. REV 00 2. Payee The payee is the person to whom the payment is to be made. 3. Date of the note The date of the note is the date on which the note is made. 4. Term of the note The term of the note is the length of time until the note is due for payment. QMT 3301 BUSINESS MATHEMATICS 3 REV 00 5. Face value The face value of the note is the amount stated on the note. 6. Maturity value The maturity value of the note is the total sum of money which the payee will receive on the maturity date. The maturity value of a non-interest bearing note is the face value while the maturity value of an interest-bearing note is the face value plus day interest that is due. 7. Maturity date The maturity date of the note is the date on which the maturity value is due. QMT 3301 BUSINESS MATHEMATICS 4 REV 00 Example of Promissory Note: RM 2500.00 20 APRIL 2008 Sixty days after date I promise to pay the order of Mohammed Ali Ringgit Malaysia: Two thousand five hundred only for value received with interest at the rate of 8.00% per annum until paid. No. 1234 Due: 19 June 2008 Mat Jenin QMT 3301 BUSINESS MATHEMATICS 5 REV 00 Example 1: From the promissory note show in the example, a) Who is the maker of the note, b) Who is the payee of the note? Calculate the maturity value of the note. Solution: a) The maker is Mat Jenin. b) The payee is Mohammed Ali. Maturity value = face value + interest due = 2500 + [2500 x 0.08 x (60/360)] = RM 2533.33 QMT 3301 BUSINESS MATHEMATICS 6 REV 00 Example 2: The maturity value of a 90-day interest bearing promissory note is RM 1200. If the interest rate is 6% per annum, what is the face value of the note? Solution: S = P(1 + rt) 1200 = P[1 + 0.06 x (90/360)] 1200 = P(1.015) P = RM 1182.27 QMT 3301 BUSINESS MATHEMATICS 7 REV 00 Example 3: The interest rate on a 60-day promissory note is RM 50. If the interest rate is 5% per annum, find the face value of the note. Solution: I = Prt 50 = P x 0.05 x (60/360) 50 = P(0.008333333333) P = RM 6000 QMT 3301 BUSINESS MATHEMATICS 8 8.2 Bank Discount REV 00 Bank discount is computed in much the same way as simple interest except that it is based on the final amount (to be paid back) or maturity value. − Formula: D = Sdt Where: D = Bank discount S = Amount of maturity value d = Discount value t = Term of discount in years QMT 3301 BUSINESS MATHEMATICS 9 REV 00 Bank proceeds is the net amount received by the borrower. − Formula: Bank proceeds = Maturity Value – Bank Discount P=S–D P = S – Sdt P = S(1 – dt) QMT 3301 BUSINESS MATHEMATICS 10 REV 00 Example 1: Alex borrows RM 6500 for 4 months from a lender who charges a discount rate of 9%. Find, a) The discount, and b) The proceeds. Solution: a) D = Sdt = 6500 x 0.09 x (120/360) = RM 195 QMT 3301 BUSINESS MATHEMATICS b)P = S – D = 6500 –195 = RM 6305 11 REV 00 Example 2: If Sharizan needs RM 5000 now, how much should he borrow from his bank for 2 years at a 4% bank discount rate? Solution: P = S(1 – dt) 5000 = S(1 – (0.04 x 2)) 5000 = S(0.92) S = RM 5434.78 QMT 3301 BUSINESS MATHEMATICS 12 REV 00 Example 3: Sheela receives an invoice of RM 2000 with cash discount terms 3/10, n/40. a) How much should be borrowed for 30 days from a bank that charges a 9% discount rate to take advantage of the cash discount? b) How much will be saved by borrowing the money to take advantage of the cash discount? QMT 3301 BUSINESS MATHEMATICS 13 REV 00 Solution: a) Cash discount offer = 2000 x 3% = RM 60 To get proceeds of RM 1940 (RM 2000 – RM 60), she should borrow more than RM 1940. Let the amount borrowed for 30 days be S ringgit. P = S(1 – dt) 1940 = S[1 –( 0.09 x (30/360))] S = RM 1954.66 QMT 3301 BUSINESS MATHEMATICS 14 REV 00 b) Bank discount for the loan = RM 1954.66 – RM 1940 = RM 14.66 Amount that will be saved = RM 60 – RM 14.66 = RM 45.34 QMT 3301 BUSINESS MATHEMATICS 15 REV 00 Example 4: Find the present value of RM 1000 due in 3 years at a) A simple interest rate of 6%, and b) A simple discount at 6%. Solution: a) b) P = S(1 + rt)-1 P = 1000(1 + (0.06 x 3))-1 P = RM 847.46 P = S(1 – dt) P = 1000(1 – (0.06 x 3)) P = RM 820 QMT 3301 BUSINESS MATHEMATICS 16 8.3 Simple Interest Rate Equivalent to REV 00 Bank Discount Rate At interest rate, r% and a discount rate, d% are said to be equivalent if the two rates give the same present value for an amount due in the future. If the present value is S, then the present value of S, at r% simple interest rate is S(1 + rt)-1 and the present value of S, at d% bank discount rate is S(1 – dt). Equating the two present value, we get: QMT 3301 BUSINESS MATHEMATICS 17 REV 00 S(1 + rt)-1 = S(1 – dt) 1 = 1 – dt 1 + rt Solving for d, we get dt = 1 – 1 1 + rt dt = rt 1 + rt d= r 1 + rt QMT 3301 BUSINESS MATHEMATICS 18 REV 00 Solving for r, we get 1 + rt = 1 1 – dt rt = 1 1 – dt rt = dt 1 – dt r= d 1 - dt -1 QMT 3301 BUSINESS MATHEMATICS 19 REV 00 Example 1: A bank discounts a RM 3000 note due in 3 months using a bank discount rate of 8%. Find the equivalent simple interest rate that is charges by the bank. Solution: r= d 1 – dt r= 0.08 [1 – (0.08 x (90/360))] = 8.16% QMT 3301 BUSINESS MATHEMATICS 20 REV 00 Example 2: What discount rate should a lender charge to earn an interest rate of 15% on a 6 months loan? Solution: d= r 1 + rt d= 0.15 [1 + (0.15 x (180/360))] d = 13.95% QMT 3301 BUSINESS MATHEMATICS 21 REV 00 8.4 Discounting Promissory Notes A promissory note can be sold to a bank before its maturity date if the holder is in need of cash. Selling the note to the bank is called discounting the note. The amount received on the date of discounting is called the proceeds. The proceeds of a promissory note are computed as follows: QMT 3301 BUSINESS MATHEMATICS 22 REV 00 a) Find the maturity value of the note. For non-interest bearing note, it is the face value. If the note is interest bearing, then Maturity value = Face Value + Interest b) Find the bank discount, D with the formula D = Sdt c) Compute the proceeds Proceeds = Maturity Value – Bank Discount QMT 3301 BUSINESS MATHEMATICS 23 REV 00 Example : Mr. Lee received a promissory note for RM 2600 with interest at 8% per annum that was due in 180 days. The note was dated 20 June 2005. The note was discounted on 24 July 2005 at a bank that charges 11% discount. Determine a) The maturity date, b) The maturity value, c) The discount period, and d) The proceeds. QMT 3301 BUSINESS MATHEMATICS 24 REV 00 Solution: a) Maturity date = 20 June 2005 + 180 days = 17 December 2005 b) Maturity value = P(1 + rt) = 2600[1 + (0.08 x (180/360))] = RM 2704 c) Discount period = 24 July 2005 to 17 Dec 2005 = (7+31+30+31+30+17) = 146 days QMT 3301 BUSINESS MATHEMATICS 25 REV 00 d) D = Sdt = 2704 (0.12 x (174/360)) = RM 156.83 Proceeds = Maturity value – Bank discount = 2704 – 156.83 = RM 2547.17 QMT 3301 BUSINESS MATHEMATICS 26
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