Chapter 10, Problem 24AT

### 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 solve for the missing information. 24. $8,000 11 Jan.12 83 _____ Mar. 1 _____ 15 To determine To calculate: The maturity date, maturity value, discount period and proceeds of the promissory note where face value is$8,000, the interest rate is 11% for 83 days. On 1 March, the note was discounted at the rate 15%. The date of the note is 12 January.

Explanation

Given Information:

Face value is $8,000, the interest rate is 11% for 83 days. On 1 March, the note was discounted at the rate 15%. The date of the note is 12 January. Formula used: 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. Subtract the number of days remaining in the first month from the total duration of the 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. Divide T by 360 to convert days into years. 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 the 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 compute the amount of bank discount is, Bank Discount=Face value×Discount Rate×Time The formula to calculate the amount of proceeds is, Proceeds=Face 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=3112=19 Subtract the number of days left that were left when the loan was taken from the total duration of the loan as: Number of days left=8319=64 In the month of February and March, there are 59 days. So, out of 64 days remaining 59 will be utilized by the months of February and March. Now, Total number of remaining days is 5. So, the Maturity date is April 5. Consider that principal amount is$8,000, the rate of interest is 11%, the time duration is 83 days.

Simplify the rate of interest as

11%=11100=0.11

Substitute $8,000 for the principal amount, 0.11 for the rate of interest, 83360 for time duration in the formula MV=P(1+RT) to compute the maturity value: MV=P(1+RT)=$8,000(1+0.11×83360)=\$8,000(1+0

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