Final answer:
Brenda's return on the 90-day T-bill will be $394 with an annualized rate of 6.5%. For bonds, with a rise in interest rates, one would pay less than the original value for the bond due to a less attractive fixed interest rate compared to new rates. The present value of bonds changes inversely with the interest rate.
Step-by-step explanation:
Brenda purchased a 25,000, 90-day T-bill for $24,606. The return Brenda will receive when the T-bill matures is the face value of the T-bill minus the purchase price. Therefore, her return is $25,000 - $24,606 = $394.
To calculate the annualized rate of return, we use the formula: Annualized Rate = (Return / Purchase Price) * (365 / Days to Maturity). Plugging in Brenda's values, we get: Annualized Rate = ($394 / $24,606) * (365 / 90) = 0.01603 * 4.05556 = 0.065 or 6.5%.
Concerning the question including bonds, if the local water company issued a $10,000 ten-year bond at an interest rate of 6%:
- a. With the interest rates now being 9%, you would expect to pay less than $10,000 for this bond because its fixed interest payments are less attractive compared to new bonds paying the higher 9% rate.
- b. The amount you would be willing to pay is the present value of the $600 interest payment plus the $10,000 principal repayment discounted back at the new market rate of 9%. This is calculated using the present value formula, giving us a price less than $10,000.
For the simple two-year bond issued at $3,000 with an 8% interest rate:
- The present value of the bond at the same 8% rate would equal the sum of the discounted interest payments and principle, which would be $3,000 since it matches the discount rate.
- However, if the discount rate rises to 11%, the present value of the bond would decrease because the future cash flows from the bond would be discounted at a higher rate, hence you would pay less than $3,000 for the bond.