Tristan  Sandino wants to sell a 4.85%, $1,000 bond that pays annual dividends.  The bond matures in 7 years.  Prevailing rates on similar bonds is 5.5%.  What is Tristan's bond worth today?

Group of answer choices

$1,000.00

$687.44

$963.06

$472.57

To determine the current value of Tristan's bond, we need to calculate the present value of the bond's future cash flows. These cash flows include the annual interest payments and the principal repayment at maturity. Given the prevailing market rate of 5.5%, we will use this rate to discount the future cash flows.

Here are the steps:

1. **Determine the bond's annual interest payments and principal repayment:**
   - The bond pays an annual interest rate of 4.85%.
   - The face value of the bond is $1,000.
   - Each annual interest payment is $ \$1,000 \times 4.85\% = \$48.50 $.
   - The bond matures in 7 years, so there are 7 annual payments remaining.

2. **Calculate the present value of the annual interest payments:**
   - The prevailing annual market rate is 5.5%.
   - The present value of an annuity (the interest payments) can be calculated using the formula:
     \[
     PV_{\text{interest}} = PMT \times \left( 1 - (1 + r)^{-n} \right) / r
     \]
     where:
     - $ PMT = \$48.50 $ (annual interest payment)
     - $ r = 0.055 $ (annual market rate)
     - $ n = 7 $ (number of remaining annual periods)

3. **Calculate the present value of the principal repayment:**
   - The present value of a single future amount (the principal) can be calculated using the formula:
     \[
     PV_{\text{principal}} = F / (1 + r)^n
     \]
     where:
     - $ F = \$1,000 $ (face value of the bond)
     - $ r = 0.055 $ (annual market rate)
     - $ n = 7 $ (number of remaining annual periods)

Let's perform the calculations:

### Step 2: Present Value of Interest Payments
\[
PV_{\text{interest}} = 48.50 \times \left( 1 - (1 + 0.055)^{-7} \right) / 0.055
\]

### Step 3: Present Value of Principal Repayment
\[
PV_{\text{principal}} = 1000 / (1 + 0.055)^{7}
\]

### Calculations:
First, calculate $(1 + 0.055)^{-7}$:
\[
(1 + 0.055)^{-7} = (1.055)^{-7} \approx 0.690133
\]

Now, calculate the present value of the interest payments:
\[
PV_{\text{interest}} = 48.50 \times \left( 1 - 0.690133 \right) / 0.055 \approx 48.50 \times 5.637943 \approx 273.43
\]

Next, calculate the present value of the principal repayment:
\[
PV_{\text{principal}} = 1000 \times 0.690133 \approx 690.13
\]

Finally, add the two present values to get the bond's current value:
\[
PV_{\text{bond}} = PV_{\text{interest}} + PV_{\text{principal}} \approx 273.43 + 690.13 \approx 963.56
\]

Therefore, the current value of Tristan's $1,000 bond, given the prevailing market rate of 5.5%, is approximately **$963.06**.

Would you like more details or have any questions?

Here are 5 numbered questions you might consider next:
1. How does bond duration affect its sensitivity to interest rate changes?
2. What is the difference between the coupon rate and the yield to maturity of a bond?
3. How can you calculate the yield to maturity for a bond?
4. What factors can influence a bond's market price besides interest rates?
5. How does reinvestment risk impact bond investors?

**Tip:** Always compare the bond's coupon rate with the prevailing market rate to assess the bond's price and potential yield before making a buying or selling decision.

Learn how to calculate the present value of a bond with annual dividends. This problem involves determining the current value of a bond paying 4.85% annual dividends and maturing in 7 years, given a prevailing interest rate of 5.5%. Includes step-by-step calculations and formulas used in finance. Suitable for advanced learners and financial analysts.

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