Solved on Nov 27, 2023

Calculate the purchase price of a 26-week T-bill with a $1000 maturity value and 5.25% annual interest rate, rounded to the nearest cent using 360 days.

STEP 1

Assumptions1. The maturity value of the-bill is $1000. The annual interest rate is5.25%
3. The-bill has a26-week term4. We are using a360-day year for the calculations5. The interest is calculated as a one-time payment, not compounding

STEP 2

First, we need to find the interest amount on the-bill. We can do this by multiplying the maturity value by the annual interest rate and the fraction of the year that the-bill is held.
$Interest = Maturity\, value \\times Annual\, interest\, rate \\times \frac{Number\, of\, days}{360}$

STEP 3

Now, plug in the given values for the maturity value, annual interest rate, and number of days (26 weeks =182 days) to calculate the interest.
$Interest = \$1000 \\times5.25\% \\times \frac{182}{360}$

STEP 4

Convert the percentage to a decimal value.
$.25\% =0.052$ $Interest = \$1000 \\times0.052 \\times \frac{182}{360}$

STEP 5

Calculate the interest amount.
$Interest = \$1000 \\times0.0525 \\times \frac{182}{360} = \$26.56$

STEP 6

Now that we have the interest amount, we can find the purchase price of the-bill. This is done by subtracting the interest from the maturity value.
$Purchase\, price = Maturity\, value - Interest$

STEP 7

Plug in the values for the maturity value and the interest to calculate the purchase price.
$Purchase\, price = \$1000 - \$26.56$

STEP 8

Calculate the purchase price of the-bill.
$Purchase\, price = \$1000 - \$26.56 = \$973.44$ The purchase price of the26-week-bill with a maturity value of $1000 that earns an annual interest rate of5.25% is$ 973.44.

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Calculate the purchase price of a 26-week T-bill with a $1000 maturity value and 5.25% annual interest rate, rounded to the nearest cent using 360 days.

STEP 1

Assumptions1. The maturity value of the-bill is $1000. The annual interest rate is5.25%
3. The-bill has a26-week term4. We are using a360-day year for the calculations5. The interest is calculated as a one-time payment, not compounding

STEP 2

First, we need to find the interest amount on the-bill. We can do this by multiplying the maturity value by the annual interest rate and the fraction of the year that the-bill is held.
$Interest = Maturity\, value \\times Annual\, interest\, rate \\times \frac{Number\, of\, days}{360}$

STEP 3

Now, plug in the given values for the maturity value, annual interest rate, and number of days (26 weeks =182 days) to calculate the interest.
$Interest = \$1000 \\times5.25\% \\times \frac{182}{360}$

STEP 4

Convert the percentage to a decimal value.
$.25\% =0.052$ $Interest = \$1000 \\times0.052 \\times \frac{182}{360}$

STEP 5

Calculate the interest amount.
$Interest = \$1000 \\times0.0525 \\times \frac{182}{360} = \$26.56$

STEP 6

Now that we have the interest amount, we can find the purchase price of the-bill. This is done by subtracting the interest from the maturity value.
$Purchase\, price = Maturity\, value - Interest$

STEP 7

Plug in the values for the maturity value and the interest to calculate the purchase price.
$Purchase\, price = \$1000 - \$26.56$

STEP 8

Calculate the purchase price of the-bill.
$Purchase\, price = \$1000 - \$26.56 = \$973.44$ The purchase price of the26-week-bill with a maturity value of $1000 that earns an annual interest rate of5.25% is$ 973.44.

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Calculate the purchase price of a 26-week T-bill with a $1000 maturity value and 5.25% annual interest rate, rounded to the nearest cent using 360 days.

STEP 1

Assumptions1. The maturity value of the-bill is $1000. The annual interest rate is5.25%3. The-bill has a26-week term4. We are using a360-day year for the calculations5. The interest is calculated as a one-time payment, not compounding

STEP 2

STEP 3

Now, plug in the given values for the maturity value, annual interest rate, and number of days (26 weeks =182 days) to calculate the interest.Interest=$1000times5.25%times182360Interest = \$1000 \\times5.25\% \\times \frac{182}{360}Interest=$1000times5.25%times360182​

STEP 4

Convert the percentage to a decimal value..25%=0.052.25\% =0.052.25%=0.052Interest=$1000times0.052times182360Interest = \$1000 \\times0.052 \\times \frac{182}{360}Interest=$1000times0.052times360182​

STEP 5

Calculate the interest amount.Interest=$1000times0.0525times182360=$26.56Interest = \$1000 \\times0.0525 \\times \frac{182}{360} = \$26.56Interest=$1000times0.0525times360182​=$26.56

STEP 6

Now that we have the interest amount, we can find the purchase price of the-bill. This is done by subtracting the interest from the maturity value.Purchase price=Maturity value−InterestPurchase\, price = Maturity\, value - InterestPurchaseprice=Maturityvalue−Interest

STEP 7

Plug in the values for the maturity value and the interest to calculate the purchase price.Purchase price=$1000−$26.56Purchase\, price = \$1000 - \$26.56Purchaseprice=$1000−$26.56

STEP 8

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The maturity value of the-bill is $1000. The annual interest rate is5.25%
3. The-bill has a26-week term4. We are using a360-day year for the calculations5. The interest is calculated as a one-time payment, not compounding

Now, plug in the given values for the maturity value, annual interest rate, and number of days (26 weeks =182 days) to calculate the interest.
$Interest = \$1000 \\times5.25\% \\times \frac{182}{360}$

Convert the percentage to a decimal value.
$.25\% =0.052$ $Interest = \$1000 \\times0.052 \\times \frac{182}{360}$

Calculate the interest amount.
$Interest = \$1000 \\times0.0525 \\times \frac{182}{360} = \$26.56$

Now that we have the interest amount, we can find the purchase price of the-bill. This is done by subtracting the interest from the maturity value.
$Purchase\, price = Maturity\, value - Interest$

Plug in the values for the maturity value and the interest to calculate the purchase price.
$Purchase\, price = \$1000 - \$26.56$