ch11_ppt

Business Math, Eighth EditionCleaves/Hobbs 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

11.1 The Simple Interest FormulaFind 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.


Key TermsInterest: 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.


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 = P x R x T


Find the simple interest using the simple interest formula


Identify the principal, rate and time

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)


Find the interest paid on a loanPrincipal = (P) $1,200Interest rate = 8% (or 0.08)Time = 1 yearInterest = P x R x TInterest = 1,200 x 0.08 x 1Interest = $96The interest on the loan is $96.


Try these examplesFind 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


11.1.2 Find the Maturity Value of a LoanMaturity 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 + PRTMV = P(1+RT)


Look at this exampleMarcus Frank Lampard 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 ( 1 + 0.09 x 2)(See next slide)


What is the maturity value?MV = $2,500 ( 1 + 0.09 x 2)MV = $2,500 (1 + 0.18)MV = $2,500 (1.18)MV = $2,950 Marcus will pay $2,950 at the end of two years.


Try these examplesTerry Williams is going to borrow $4,000 at 7.5% interest. What is the maturity value of the loan after three years?$4,900

Jim Sherman will invest $3,000 at 8% for 5 years. What is the maturity value of the investment?$4,200


11.1.3 Convert Months to a Fractional or Decimal Part of a YearWrite the number of months as the numerator of a fraction.Write 12 as the denominator of the fraction.Reduce the fraction to lowest terms if using the fractional equivalent.Divide the numerator by the denominator to get the decimal equivalent of the fraction.


Convert the following to fractional or decimal part of a yearConvert 9 months and 15 months, respectively, to years, expressing both as fractions and decimals.9/12 = = 0.759 months = or 0.75 of a year15/12 = 1 3/12 = 1 = 1.2515 months = 1 or 1.25 of a year.


Look at this exampleTo save money, Stan Wright invested $2,500 for 42 months at 4 % simple interest. How much interest did he earn?42 months = 42/12 = 3.5I = P x R x TI = $2,500 x 0.045 x 3.5I = $393.75Stan will earn $393.75


Try these examplesAkiko is saving a little extra money to pay for her car insurance next year. If she invests $1,000 for 18 months at 4%, how much interest can she earn?$60

Habib is going to borrow $2,000 for 42 months at 7% . What will the amount of interest owed be?$490


11.1.4 Find the Principal, Rate or Time Using the Simple Interest Formula


Find the principal using the simple interest formulaP = I / RTJudy paid $108 in interest on a loan that she had for 6 months. The interest rate was 12%. How much was the principal?Substitute the known values and solve.P = 108/ 0.12 x 0.5P = $1,800


R = I / PTSam wants to borrow $1,500 for 15 months and will have to pay $225 in interest. What is the rate he is being charged?Substitute the known values and solve.R = 225/ $1,500 x 1.25R = .12 or 12%The rate Sam will pay is 12%. Find the rate using the simple interest formula


T = I / RPShelby borrowed $10,000 at 8% and paid $1,600 in interest. What was the length of the loan?Substitute the known values and solve.T = $1,600/0.08 x $10,000T = 2The length of the loan was two years.Find the time using the simple interest formula


11.2 Ordinary and Exact InterestFind exact time.

Find the due date.

Find the ordinary interest and the exact interest.

Make a partial payment before the maturity date.


11.2.1 Find Exact TimeOrdinary time: time that is based on counting 30 days in each month.

Exact time: time that is based on counting the exact number of days in a time period.


ExamplesThe ordinary time from July 12 to September 12 is 60 days.To find the exact time from July 12 to September 12, add the following:Days in July (31 - 12 =) 19Days in August 31Days in September+12 62 days


Sequential Numbers for Dates of the YearFind the exact time of a loan using the sequential numbers table. (Table 11-1 in the text)If the beginning and due dates of the loan fall within the same year, subtract the beginning dates sequential number from the due dates sequential number.Ex.: From May 15 to October 15288-135 = 153 days is the exact time


Beginning and due dates in different yearsSubtract the beginning dates sequential number from 365.

Add the due dates sequential number to the result from the previous step.

If February 29 falls between the two dates, add 1. (Is it a leap year?)


Look at this exampleFind the exact time from May 15 on Year 1 to March 15 in Year 2.365 135 = 230230 + 74 = 304 daysThe exact time is 304 days.Note: If Year 2 is a leap year, the exact time is 305 days.


Try this exampleA loan made on September 5 is due July 5 of the following year. Find: a) ordinary time b) exact time in a non-leap year c) exact time in a leap year.Ordinary time = 300 daysExact time (non-leap year) = 303 daysExact time (leap year) = 304 days


11.2.3 Find the Ordinary Interest and the Exact InterestOrdinary interest: a rate per day that assumes 360 days per year.Exact interest: a rate per day that assumes 365 days per year.Bankers rule: calculating interest on a loan based on ordinary interest and exact time which yields a slightly higher amount of interest.


Find the ordinary interest per dayFor ordinary interest rate per day, divide the annual interest rate by 360.Ordinary interest rate per day = Interest rate per year360


Find the exact interest per dayFor exact interest rate per day, divide the annual interest rate by 365.Exact interest rate per day = Interest rate per year 365


Use ordinary time to find the ordinary interest on a loanA loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x TLength of loan (ordinary time) = 60 daysRate = 0.07/360 (ordinary interest)Interest = $500 x 0.07/360 x 60Interest = $5.83


Find the ordinary interest using exact time for the previous loanA loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x TLength of loan (exact time) = 61 daysRate = 0.07/360 (ordinary interest)Interest = $500 x 0.07/360 x 61Interest = $5.93


Find the exact interest using exact time for the previous loanA loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x TLength of loan (exact time) = 61 daysRate = 0.07/365 (exact interest)Interest = $500 x 0.07/365 x 61Interest = $5.84


11.2.4 Make a Partial Payment Before the Maturity DateTo find the adjusted principal and adjusted balance due at maturity for a partial payment made before the maturity date:1.Determine the exact time from the date of the loan to the first partial payment.

2.Calculate the interest using the time found in Step 1.

(continue on next slide)


11.2.4 Make a Partial Payment Before the Maturity Date3. Subtract the amount of interest found in Step 2 from the partial payment. 4.Subtract the remainder of the partial payment (Step 3) from the original principal. This is the adjusted principal.5.Repeat process for additional partial payments.6. At maturity, calculate interest from the last partial payment and add to adjusted principal. This is the adjusted balance due at maturity.


Look at this exampleTony borrows $5,000 on a 10%, 90 day note. On the 30th day, Tony pays $1,500 on the note. If ordinary interest is applied, what is Tonys adjusted principal after the partial payment, and adjusted balance due at maturity?$5,000(.1)(30/360) = $41.67 $1,500 - $41.67 = $1,458.33$5,000 - $1,458.33 = $3,541.67 (Adj. Principal)$3,541.67(.1)(60/360) = $59.03 (Interest)$3,541.67 + $59.03 = $3,600.70 (Adj. Balance)


11.3 Promissory NotesFind the bank discount and proceeds for a simple discount note.

Find the true effective interest rate of a simple discount note.

Find the third-party discount and proceeds for a third-party discount note.


11.3.1 Find the Bank Discount and Proceeds for a Simple Discount NoteFor 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


A promissory note


11.3.2 Find the True of Effective Interest Rate of a Simple Discount NoteTo find the true or effective interest rate of a simple discount note:1.Find the bank discount (interest). I = PRT2.Find the proceeds: proceeds = principal bank discount.3. Find the effective interest rate: R = I/PT using the proceeds as the principal


Try this exampleWhat is the effective interest rate of a $5,000 simple discount note, at an ordinary bank discount rate of 12%, for 90 days?I = PRT; I = $5,000(.12)(90/360)I = $150 (Bank discount)Proceeds = $5,000 - $150 = $4,850R = I/PT; R = $150/$4,850(90/360)R = .1237113402R or the effective interest rate = 12.4%


11.3.3 Find the Third Party Discount and Proceeds for a Third Party Discount NoteFor 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


Look at this exampleMihoc Trailer 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 needs cash, the note is taken to a third party on September 5.The third-party agrees to accept the note with a 13% annual discount using the bankers rule.Find the proceeds of the note.


Mihoc Trailer SalesTo 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 ( 1 + 0.09/365 x 90)

MV = $10.221.92


Find the proceeds of the noteExact time of the discount period is 66 days. (314 - 248) period between Sept. 5 and Nov. 10.Ordinary discount rate is 0.13/ 360.Third party discount = I = PRTThird party discount = $10,221.92 (0.13/360)(66)Third party discount = $243.62Proceeds = A = P IProceeds = $10,221.92 - $243.62 = $9,978.30

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