Final answer:
The present value of a $3,000 bond paying 8% annual interest is calculated for two years under two different discount rates, 8% and 11%. The present value is the total of the discounted payments received from the bond each year. The calculated present value reflects what the future payments are worth in today's dollars.
Step-by-step explanation:
The question regards calculating the present value of a bond with different discount rates using the present value formula. The bond in question is a simple two-year bond with a principal amount of $3,000 and an 8% annual interest rate. For the first year, this bond will pay $240 in interest, and at the end of the second year, the bond pays another $240 in interest along with the $3,000 principal. When the discount rate is 8%, the present value calculations are as follows:
- First year interest: $240 / (1 + 0.08)¹ = $222.22
- Second-year payment: $3,240 / (1 + 0.08)² = $2,777.78
- Total present value at 8% discount rate: $222.22 + $2,777.78 = $3,000
However, if interest rates rise and the discount rate becomes 11%, the present value calculations for the bond would change:
- First year interest: $240 / (1 + 0.11)¹
- Second-year payment: $3,240 / (1 + 0.11)²
- Total present value at 11% discount rate would need to be calculated based on the above components.