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Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

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BuyFindarrow_forward

Contemporary Mathematics for Busin...

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

Using ordinary interest, 360 days, calculate the bank discount, proceeds, and effective rate for the following simple discount notes. Round effective rate to the nearest hundredth of a percent.

Face Discount Term Bank Effective
Value Rate (%) (days) Discount Proceeds Rate (%)
14. $95,000 9.7 45 __________ ____________ _______________

To determine

To calculate: The amount of bank discount, proceeds value and effective rate of interest where face value is $95,000, discount rate is 9.7%, time period is 45 days.

Explanation

Given Information:

Face value is $95,000, discount rate is 9.7%, time period is 45 days.

Formula used:

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=Face value×Discount Rate×Time

The formula to calculate amount of proceeds is,

Proceeds=Face valueDiscount

The formula to calculate effective rate of interest is,

Effective interest rate=InterestPurchase Price×Time

Calculation:

Consider the face value of loan is $95,000, discount rate is 9.7% and time period is 45 days.

Compute the discount amount,

Simplify the discount rate as,

9.7%=9.7100=0.097

Evaluate the time as,

Time=Number of days of a loan360=45360

Substitute $95,000 for face value, 0.097 for discount rate and 45360 for time in the formula

Bank Discount=Face value×Discount Rate×Time” as,

Bank Discount=Face value×Discount Rate×Time=95,000×0.097×45360=$1,151

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