To determine if you should buy the bond, you will need to calculate the present value of the $10,000 payment you will receive in 4 years, using the given interest rate of 6%.
The formula to calculate the present value (PV) is:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \(FV\) is the future value ($10,000 in this case),
- \(r\) is the interest rate (6% or 0.06),
- \(n\) is the number of years until payment (4 years).
Plugging in these values, we get:
\[ PV = \frac{10000}{(1 + 0.06)^4} \] \[ PV = \frac{10000}{(1.26247696)} \] \[ PV \approx \frac{10000}{1.26247696} \approx 7,936.54 \]
So, the present value of the bond is approximately $7,936.54. You should buy the bond if its price today is no greater than this amount.
Let's compare this value with the options given:
- a. $8,225.06 - too high
- b. $6,998.98 - acceptable
- c. $7,920.94 - acceptable
- d. $7,672.58 - acceptable
Since $7,936.54 is higher than all values except a, you should buy the bond if the price today is no greater than approximately $7,936.54. Therefore, the options that work are b, c, or d, but not a.
However, the answer that is closest but still ≤ $7,936.54 is c. $7,920.94.
Final Answer: c. $7,920.94.