Final answer:
Interest on a 91-day T-bill quoted as "3" cannot be determined without the face value and purchase price. The cash price is the face value minus the discounted amount over 91 days. For a two-year bond with an 8% interest rate, present value calculations are based on the discount rates and future payments.
Step-by-step explanation:
To calculate interest earned on a 91-day Treasury bill (T-bill) that is quoted as "3", we use the following formula:
Interest = (Face Value - Price) / Price * (360 / Days to Maturity)
However, without the face value and the exact price at which the T-bill was purchased, we cannot calculate the interest in dollars. The '3' represents a discount yield, but more information is needed for a precise calculation.
For the cash price, we can extract from the question that it is quoted as a discount rate of 3%. The cash price can be calculated by subtracting the discount from the face value. Since the actual face value isn't provided, we use a placeholder (FV) for face value to demonstrate the calculation:
Cash Price = FV - (FV * (3/100) * (91/360))
Now, let's apply these concepts to a bond example. A two-year bond issued at $3,000 with an 8% interest rate would pay $240 in interest annually. To find the present value of the bond with an 8% discount rate, we calculate the present value of each payment separately:
Present Value Year 1 = $240 / (1 + 0.08)
Present Value Year 2 = ($3,000 + $240) / (1 + 0.08)^2
With an 11% discount rate, we simply replace 0.08 with 0.11 in the above formula. The present value calculations consider both the interest payments and the principal repayment.