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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

Calculate the interest, purchase price, and effective interest rate of the following Treasury bill (T-bill) purchases. Round effective interest rate to the nearest hundredth of a percent.

Face Discount Term Purchase Effective
Value Rate (%) (weeks) Interest Price Rate (%)
21. $ 15.000 5,20 13 $195 $14,805 5.27

To determine

To calculate: The amount of bank interest, purchase price and effective rate of interest where face value is $15,000, discount rate is 5.20%, time period is 13 weeks.

Explanation

Given Information:

Face value is $15,000, discount rate is 5.20%, time period is 13 weeks.

Formula used:

The formula to calculate the time is,

Time=Number of weeks of a loan52

The formula to compute the amount of bank interest is,

Bank interest=Face value×Discount Rate×Time

The formula to calculate purchase price is,

Purchase Price=Face valueInterest

The formula to calculate effective rate of interest is,

Effective interest rate=InterestPurchase Price×Time

Calculation:

Consider that face value of loan is $15,000, discount rate is 5.20% and time period is 13 weeks.

Compute the interest amount,

Simplify the interest rate as,

5.20%=5.20100=0.052

Evaluate the time as,

Time=Number of weeks of a loan52=1352

Substitute $15,000 for face value, 0.052 for discount rate and 1352 for time in the formula

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

Bank interest=Face value×Discount Rate×Time=15,000×0.052×1352=$195

Hence, amount of interest is $195

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