49 Business Math _ 123

Business Math Chapter 11: Simple Interest and Simple Discount 11.1 The Simple Interest Formula  Find simple interest by using the simple interest formula  Find the maturity of a loan  Convert months to a fractional or decimal part of the year  Find the principal, rate or time using the simple interest formula Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Key Terms  Interest: an amount paid or earned for the use of money  Simple interest: interest earned when a loan or investment is repaid in a lump sum  Principal: the amount of money borrowed or invested  Rate: the percent of the principal paid as interest per time period  Time: the number of days, months or years that the money is borrowed or invested Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved 11.1.1 The Simple Interest Formula  The interest formula shows how interest, rate, and time are related and gives us a way of finding one of these values if the other three values are known I=PxRxT Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the simple interest using the simple interest formula Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Identify the principal, rate and time P= R x B  The interest is a percentage  Principal is the amount borrowed or invested  Rate of interest is a percent for a given time period, usually one year  Time must be expressed in the same unit of time as the rate (i.e one year) Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the interest paid on a loan  Principal = (P) $1,500  Interest rate = 9% (or 0.09)  Time = year  Interest = P x R x T  Interest = 1,500 x 0.09 x  Interest = $135  The interest on the loan is $135 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Try these examples  Find the interest on a 2-year loan of $4,000 at a 6% rate  $480  Find the interest earned on a 3-year investment of $5,000 at 4.5% interest  $675 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved 11.1.2 Find the maturity value of a loan  Maturity value: the total amount of money due by the end of a loan period; the amount of the loan and interest  If the principal and the interest are known, add them  MV = principal + PRT  MV = P(1+RT) Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Look at this example  Marcus Logan can purchase furniture on a 2-year simple interest loan at 9% interest per year  What is the maturity value for a $2,500 loan?  MV = P (1 + RT) Substitute known values  MV = $2,500 ( + 0.09 x 2) (See next slide) 10 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the ordinary interest per day  For ordinary interest rate per day, divide the annual interest rate by 360 Ordinary interest rate per day = Interest rate per year 360 29 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the exact interest per day  For exact interest rate per day, divide the annual interest rate by 365 Exact interest rate per day = Interest rate per year 365 30 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Use ordinary time to find the ordinary interest on a loan  A loan of $500 at 7% annual interest rate The loan was made on March 15 and due on May 15 (Principal = $500) I =PxRxT  Length of loan (ordinary time) = 60 days  Rate = 0.07/360 (ordinary interest)  Interest = $500 x 0.07/360 x 60  Interest = $5.83 31 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the ordinary interest using exact time for the previous loan  A loan of $500 at 7% annual interest rate The loan was made on March 15 and due on May 15 (Principal = $500) I =PxRxT  Length of loan (exact time) = 61 days  Rate = 0.07/360 (ordinary interest)  Interest = $500 x 0.07/360 x 61  Interest = $5.93 32 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the exact interest using exact time for the previous loan  A loan of $500 at 7% annual interest rate The loan was made on March 15 and due on May 15 (Principal = $500) I =PxRxT  Length of loan (exact time) = 61 days  Rate = 0.07/365 (exact interest)  Interest = $500 x 0.07/365 x 61  Interest = $5.84 33 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved 11.2.4 Find simple interest using a table Identify the amount of money that the table uses as the principal (Usually $1, $100 or $1000) Divide the loan principal by the table principal Select the days row corresponding to the time period (in days) of the loan (continue on next slide) 34 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find simple interest using a table Select the annual rate column corresponding to the annual interest rate of the loan Locate the value in the cell where the two intersect Multiply the quotient from step by the value from step 35 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Look at this example  Find the exact interest on a loan of $6,500 at 7.5% annually for 45 days  Use Table 11-2 in your text to locate the interest for $100 Move across the 45-days row to the 7.5% column  The number is 0.924658  Divide $6,500 by $100 ( = 65)  Multiply 0.924658 x 65 = $860.11  The exact interest is $860.11 36 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Try these examples  Find the exact interest on a $5,000 loan for 30 days at 8%  $32.88  Find the exact interest on a $1,800 loan for 20 days at 8.5%  $8.38 37 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved 11.3.1 Find the bank discount and proceeds for a simple discount note  For the bank discount, use: Bank discount = face value x disc rate x time [I = P x R x T]  For the proceeds, use: Proceeds = face value – bank discount A=P-I 38 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved A promissory note 39 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved 11.3.2 Find the third party discount and proceeds for a third party discount note  For the bank discount, use: Third party discount = maturity value of the original note x discount rate x discount period  For the proceeds, use: Proceeds = maturity value of original note – third-party discount A=P-I 40 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Look at this example  Mihoc Trailer Sales made a note of $10,000 with Darcy Mihoc,owner, at 9% simple interest based on exact interest and exact time The note is made on August 12 and due November 10 Since Mihoc Trailer Sales needs cash, the note is taken to a third party on September  The third-party agrees to accept the note with a 13% annual discount using the banker’s rule  Find the proceeds of the note 41 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Mihoc Trailer Sales  To find the proceeds, we find the maturity value of the original note, then the third-party discount  Exact time is 90 days (314-224)  Exact interest rate is 09/365  MV = P(1+ RT)  MV = $10,000 ( + 0.09/365 x 90)  MV = $10.221.92 42 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the proceeds of the note  Exact time of the discount period is 66 days (314 - 248) period between Sept and Nov 10  Ordinary discount rate is 0.13/ 360  Third party discount = I = PRT  Third party discount = $10,221.92 ( 0.13/360) (66)  Third party discount = $243.62  Proceeds = A = P – I  Proceeds = $10,221.92 - $243.62 = $9,978.30 43 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved ... Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved Find the simple interest using the simple interest formula Cleaves/Hobbs: Business. .. borrow $2,000 for 42 months at 7% What will the amount of interest owed be?  $490 16 Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All... the year  Find the principal, rate or time using the simple interest formula Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc Upper Saddle River, NJ 07458 All Rights Reserved