Question
Suppose you are deciding whether to buy a particular bond. If you buy the bond and hold it for 4 years, then at that time you will receive a payment of $10,000. If the interest rate is 6 percent, you will buy the bond if its price today is no greater than
a. $8,225.06.
b. $6,998.98.
c. $7,920.94.
d. $7,672.58.
a. $8,225.06.
b. $6,998.98.
c. $7,920.94.
d. $7,672.58.
Answers
GPT-4o mini
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:
1. a. $8,225.06 - too high
2. b. $6,998.98 - acceptable
3. c. $7,920.94 - acceptable
4. 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.**
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:
1. a. $8,225.06 - too high
2. b. $6,998.98 - acceptable
3. c. $7,920.94 - acceptable
4. 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.**