Chapter 10.III, Problem 20RE

### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

Chapter
Section

### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447
Textbook Problem

# The following interest-bearing promissory notes were discounted at a bank by the payee before maturity. Use the ordinary interest method, 360 days, to calculate the missing information. Face Interest Date of Term of Maturity Maturity Date of Discount Discount Value Rate (%) Note Note (days) Date Value Discount Period (days) Rate (%) Proceeds $1,240 7.6 Sept. 12 140 ________ ________ Dee. 5___________ 11.8 _____________ To determine To calculate: The maturity date, maturity value, discount period and proceeds of the promissory note where face value is$1,240, interest rate is 7.6% for 140 days. On 5 December, note was discounted at the rate 11.8% and the date of the note is 12 September.

Explanation

Given Information:

Face value is $1,240, interest rate is 7.6% for 140 days On 5 December, note was discounted at the rate 11.8% and the date of the note is 12 September. Formula used: Steps for determining the maturity date of a loan are: Step1. Calculate the number of days that are left in the month loan is taken by subtracting the loan date from the number of days in the month. Step2. Subtract the number of days remaining in the first month from the total duration of loan. Step3. Keep on subtracting the days from consequent months until the maturity date corresponds to the difference. The formula to calculate Maturity value is, MV=P(1+RT) Where, MV is Maturity value, P is Principal Amount, R is the rate of interest, and T is the time duration. Steps for determining number of days of a loan are: Step1. Calculate the number of days that are left in the month loan is taken by subtracting the loan date from the number of days in the month. Step2. Determine the number of days for next succeeding months. Step3. Calculate the number of days that are left in the last month till the due date. Step4. Add all the days calculated. The formula to calculate the time for ordinary interest is, Time=Number of days of a loan360 The formula to compute the amount of bank discount is, Bank Discount=Maturity value×Discount Rate×Time The formula to calculate amount of proceeds is, Proceeds=Maturity valueDiscount Calculation: Calculate the number of days that are left in the month when the loan was taken by subtracting the loan date from the number of days in the month as: Number of days left=Total days in that monthLoan Date=3012=18 Subtract the number of days left that were left when the loan was taken from the total duration of the loan as: 14018=122 In the month of October, November and December, there are total of 92 days. So, out of 122 days, 92 will be utilized by the month of October, November and December. Now, total number of remaining days are 30. So, maturity date is January 30. Consider that principal amount is$1,240, rate of interest is 7.6%, time duration is 140 days.

Simplify the rate of interest as,

9%=9100=0.09

The principal amount is same as the face value.

Compute the maturity value by substituting $1,240 for principal amount, 0.076 for rate of interest, 140360 for time duration in the formula, “MV=P(1+RT)” as, MV=P(1+RT)=$1,240(1+0.076×140360)=\$1,240(1+0

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