Quantitative Methods Chp. 10

Promissory Note

-A debt instrument in which one party agrees to repay money to another, within a specified period of time. -May be noninterest-bearing (at no interest), or interest-bearing (at a specified rate of interest).

Ordinary interest, or banker's rule

-Interest calculation method using 360 days as the time factor denominator -Time=Number of days of a loan/360

Exact Interest

-Interest calculation method using 365 days (366 in leap year) as the time factor denominator -Time=Number of days of a loan/365

Simple Discount Note

-Promissory note in which the interest is deducted from the principal at the beginning of the loan

True or Effective Interest Rate

-The actual interest rate charged on a discounted note. Takes into account the fact that the borrower does not receive the full amount of the principal. -Effective Interest Rate=Bank Discount/Proceeds*Time

Bank Discount

-The amount of interest charged (deducted from principal) on a discounted promissory note. -Bank discount=Face Value*Discount Rate*Time

Proceeds

-The amount of money that the borrower receives at the time a discounted note is made. -Proceeds = Face Value-Bank Discount

Principal

A sum of money, either invested or borrowed on which interest is calculated.

A loan date was made on April 4 and had a due date of July 18. What is the number of days of the loan?

April 30-April 4=26 days May = 31 days June = 30 days July = 18 days Days in Loan =105 days

Henry signed a $18000 simple discount promissory note. The discount rate is 11%, and the term of the note is 250 days. What is the amount of the bank discount, and what are his proceeds on the loan?

Bank Discount = FV*R*T=18000*.11*250/360=$1375.00 Proceeds= FV-BD=18000-1375.00=$16625.00

Jane signed a $20000 simple discount promissory note. The discount rate is 13%, and the term of the note is 330 days. What is the amount of the bank discount, and what are her proceeds on the loan?

Bank Discount=FV*R*T =20000*.13*330/360=$2383.33 Proceeds=FV-BD=20000-2383.33=$17,616.67

What is the effective interest rate of a simple discount note for $40000 at a bank discount rate of 11%, for a period of 270 days?

Bank Discount=FV*R*T=40000*.11*270/360=$3300 Proceeds=FV-BD=40000-3300=$36700 Effective Interest Rate=BD/Proceeds*T=3300/(36700*270/360)=.1199 or 11.99%

A firm borrowed $15000 at 12% ordinary interest for 100 days. On day 20 of the loan, it made a partial payment of $4000. On day 60, it made another partial payment of $5000. What is the final amount due on the loan?

Day 20 Partial Payment = 15000*.12*20/360=$100 Partial Payment = 4000 Interest = -100 Principal Payment= 3900 Original Principal = 15000 Principal Payment = -3900 Adjusted Principal= 11100 Day 60 Partial Payment = 11100*.12*40/360=$148 Partial Payment = 5000 Interest = -148 Principal Payment= 4852 Original Principal = 11100 Principal Payment = -4852 Adjusted Principal= 6248 I=PRT=6248*.12*40/360=$83.31 Maturity Value=P+I MV=6248+83.31=$6331.31

What is the maturity date of a loan taken out on Sep. 9 for 125 days?

Days in Sept. : 30 Loan date (Sep. 9)= - 9 Days remaining in Sep. = 21 Days of loan= 125 Days remaining in Sep. = -21 104 Days in Oct. = -31 73 Days in Nov. = -30 43 Days in Dec.= -31 Maturity Date = January 12

Using the Simple Interest Formula: The magic Triangle

I=PRT P=I/RT R=I/PT T=I/PR

What is the amount of interest for a loan of $4000, at 7% interest for 2 1/4 years?

I=PRT or I=4000*7%*2.25=$630

What is the amount of interest for a loan of $45000 at 9 3/4% interest for 3 months?

I=PRT or I=45000*9.75%*3/12=$1096.88 (9 3/4% is 9.75% or .0975)

Compound Interest

Interest calculated at regular intervals on the principal and previously earned interest.

Simple Interest

Interest calculated solely on the principal amount borrowed or invested. It is calculated only once for the entire time period of the loan.

Simple Interest Formula

Interest=Principal *Rate*Time or I=PRT

Time

Length of time, expressed in days, months, or years of an investment or loan.

A firm borrowed money at 9% interest for 125 days. If the interest charge was $560, use the ordinary interest method to calculate the amount of principal of the loan.

Ordinary Interest Method= Time=Number of days/360 P=i/rt 560/(.09*125/360)=$17920

What is the rate of interest on a loan of $25000, for 245 days, if the amount of interest is $1960, using the ordinary interest method?

Ordinary Interest Method= Time=Number of days/360 r=i/pt 1960/(25000*245/360)=.1152 =11.52%

What is the time period of a loan for $15000 at 9.5% ordinary interest, if the amount of interest is $650?

Ordinary Interest Method= Time=Number of days/360 t=i/pr 650/(15000*.095)=.4561*360=164.2=165 days

Rate

Percent that is charged or earned for the use of money per year.

Calculating Discounted Note

Step 1: Calculate the maturity value of the note. If the original note was noninterest-bearing, the maturity value will be the same as the face value. If the original note was interest-bearing, the maturity value should be calculated as usual: mv=p(1+rt) Step 2: Determine the number of days or months of the discount period. The discount period is used as the numerator of the time in Step 3. Step 3: Calculate the amount of the bank discount by using the following formula. Note: Use ordinary interest, 360 days, for discounting a note before maturity, when the terms are stated in days. bd=mv*r*t Step 4: Calculate the proceeds of the note by using the formula: proceeds = mv-bd

Calculating the number of days of a loan

Step 1: Determine the number of days remaining in the first month by subtracting the loan date from the number of days in that month. Step 2: List the number of days for each succeeding whole month. Step 3: List the number of days in the last month. Step 4: Add the days from Steps 1,2, and 3

Determining the Maturity Date of a Loan

Step 1: Find the number of days remaining in the first month by subtracting the loan date from the number of days in that month. Step 2: Subtract the days remaining in the first month (Step 1) from the number of days of the loan. Step 3: Continue subtracting days in each succeeding whole month until you reach a month with difference less than the total days in that month. At that point, the maturity date will be the day that corresponds to the difference.

Calculating Partial Payment

Step 1: Using the simple interest formula with ordinary interest, compute the amount of interest due from the date of the loan to the date of the partial payment. Step 2: Subtract the interest from Step 1 from the partial payment. This pays the interest to date. Step 3: Subtract the balance of the partial payment after Step 2 from the original principal of the loan. This gives the adjusted principal. Step 4: If another partial payment is made, repeat Steps 1,2, and 3 using the adjusted principal and the number of days since the last partial payment. Step 5: The maturity value is computed by adding the interest since the last partial payment to the adusted principal.

Loan Date

The first day of a loan.

Due Date or Maturity Date

The last day of a loan.

Interest

The price or rental fee charged by a lender to a borrower for the use of money.

Maturity Value

The total payback of principal and interest of an investment or loan.

Gabe borrows $24500, at 8%, for 119 days. If the lender calculates interest by the exact method, what is the amount of interest on the loan?

Time=Number of days of a loan/365 or I=PRT =24500*8%*119/365=$639.01

Carol borrows $13000, at 9 1/2% interest, for 200 days. If the lender uses ordinary interest method, how much interest will Sandra have to pay?

Time=number of days of a loan/360 or I=PRT= 13300*9.5%*200/360=$686.11

Formula for calculating maturity value:

When interest amount is known: --Maturity Value=Principal+Interest or --MV=P+I When interest amount is unknown: --Maturity Value=Principal (1+Rate*Time) or --MV=P(1+RT)

Months

When the time period of a loan is a specified number of months, express time factor as a fraction of a year. --The number of months is the numerator and 12 months (1 year) is the denominator. ---1/12 equals 1 months ---5/12 equals 5 months

Years

When the time period of a loan is a year or longer, use the number of years as the time factor. --2 equals 2 years, 1.5 equals 1 1/2 years

On March 25, Helen Norton received from a customer a $3200 promissory note at 12% ordinary interest for 60 days. On April 14, Helen discounted the note at the Glenside Bank at a discount rate of 15%. a) What was the maturity date of the note? b)What was the maturity value of the note? c)Determine the discount period. d)What proceeds did Helen receive on April 14?

a. May 24 b. $3264 c. 40 days d. $3209.60

What is the maturity value of a loan for $15400, at 6 1/2% simple interest, for 24 months?

i=PRT=15400*6.5%*2=$2002 MV=P+I=15400+2002=17402 Alternate Method: --MV=P(1+RT)=15400(1+.065*2)=$17402

A firm received a $35000 promissory note at 10% simple interest for 6 months fro a customer. After 4 months, the note was discounted at the bank at discount rate of 14%. What are the proceeds the firm will receive from the discounted note?

mv=p(1+rt)= 35000(1+.10*6/12)=$36750 discount period=6 months-4 months=2 months Bank Discount=mv*r*t=36750*.14*2/12=$857.50 Proceeds=mv-bd=36750=857.50=$35892.50