Question

George buys a six-month $6000 treasury bill that sells at a discount rate of 4.5%. What is the amount of the discount? What is the price of the T-bills?

a) $135
b) $270
c) $315
d) $345

Answer 1

The discount on a $6000 Treasury bill with a 4.5% discount rate is $270, and the price of the T-bill would be $5730. For bonds, when market interest rates rise, existing bonds with fixed rates typically decrease in price. The exact price to pay for such a bond would depend on the present value calculations of future payments at the new interest rate.

Step-by-step explanation:

The question pertains to the valuation of Treasury bills and bonds, which involves understanding the discount rate and calculating the present value of future payments. These concepts are crucial within the subject of finance in Mathematics.

For Treasury bills, since they are sold at a discount, we calculate the discount by applying the discount rate to the face value. Here, the discount on a $6000 T-bill at a 4.5% discount rate for six months would be $6000 * 4.5% = $270. Therefore, the price of the T-bill would be $6000 - $270 = $5730.

Regarding the bond question, when interest rates rise, the price of existing bonds usually decreases. So, given the interest rates increased from 6% to 9%, the expectation would be that you would pay less than the original issue price of $10,000 for the bond. The exact price you would be willing to pay would require calculating the present value of the remaining payments (interest and principal) using the new market interest rate.

Answer 2

To find the amount of the discount, you can use the formula:

\[ \text{Discount} = \text{Face Value} \times \text{Discount Rate} \times \left( \frac{\text{Time to Maturity}}{\text{Number of Periods in a Year}} \right) \]

Given that the face value is $6000, the discount rate is 4.5%, and the time to maturity is 6 months (or 0.5 years), the calculation is:

\[ \text{Discount} = 6000 \times 0.045 \times \left( \frac{0.5}{1} \right) \]

\[ \text{Discount} = 6000 \times 0.0225 = 135 \]

So, the amount of the discount is $135.

Now, to find the price of the T-bill, you subtract the discount from the face value:

\[ \text{Price} = \text{Face Value} - \text{Discount} \]

\[ \text{Price} = 6000 - 135 = 5865 \]

Therefore, the price of the T-bill is $5865.

The correct answer is:

a) $135