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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 (%)
24. $35,000 3.80 4

To determine

To calculate: The amount of bank interest, purchase price and effective rate of interest where face value is $35,000, discount rate is 3.80%, time period is 4 weeks.

Explanation

Given Information:

Face value is $35,000, discount rate is 3.80% and time period is 4 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 $35,000, discount rate is 3.80% and time period is 4 weeks.

Compute the interest amount,

Simplify the interest rate as,

3.80%=3.80100=0.038

Evaluate the time as,

Time=Number of weeks of a loan52=452

Substitute $35,000 for face value, 0.038 for discount rate and 452 for time in the formula

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

Bank interest=Face value×Discount Rate×Time=35,000×0.038×452=$102

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