A bond has 10 years until maturity, a coupon rate of 8.1%, and sells for $1,190. Interest is paid annually. (Assume a face value of $1,000.)

If the bond has a yield to maturity of 9.9% 1 year from now, what will its price be at that time?

**Note: Do not round intermediate calculations. Round your answer to nearest whole number.**


What will be the rate of return on the bond?

**Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.**




### To solve these questions, we'll break them down into two parts:

### 1. **Find the bond price 1 year from now** (given a yield to maturity of 9.9%)

#### Formula for Bond Price:
The price of a bond is calculated as the present value of its future coupon payments and its face value, discounted by the yield to maturity (YTM).

The formula is:
\[
P = \sum_{t=1}^{n} \left( \frac{C}{(1 + r)^t} \right) + \frac{F}{(1 + r)^n}
\]
Where:
- $ P $ = price of the bond
- $ C $ = coupon payment = face value × coupon rate = 1000 × 8.1% = $81
- $ r $ = yield to maturity (YTM) = 9.9% = 0.099
- $ F $ = face value of the bond = $1,000
- $ n $ = number of years to maturity = 9 (since 1 year has passed, leaving 9 years until maturity)

Now, we can plug in the values to find the bond price one year from now.

### 2. **Calculate the rate of return on the bond**

The rate of return on the bond can be found using the formula:
\[
\text{Rate of Return} = \frac{\text{Coupon Payment} + \left( \text{New Price} - \text{Old Price} \right)}{\text{Old Price}} \times 100
\]
Where:
- Old Price = $1,190 (current price)
- New Price = Price we calculate in part 1
- Coupon Payment = $81

Let's calculate these step by step.### Results:
1. **Price of the bond 1 year from now**: $896 (rounded to the nearest whole number).
2. **Rate of return on the bond**: -17.91% (rounded to two decimal places).

The bond's price decreases due to the higher yield to maturity, and the rate of return is negative, indicating a loss on the investment.

Would you like more details or have any further questions?

Here are some related questions to explore:

1. How does the bond price change with different coupon rates?
2. What impact does yield to maturity have on bond prices over time?
3. How does the time to maturity affect the sensitivity of bond prices to interest rate changes?
4. What is the difference between current yield and yield to maturity?
5. How do interest rate fluctuations affect the rate of return on bonds?

**Tip:** The longer the bond’s duration, the more sensitive it is to interest rate changes.

A bond has 10 years until maturity, a coupon rate of 8.1%, and sells for $1,190. Interest is paid annually. If the bond has a yield to maturity of 9.9% 1 year from now, what will its price be at that time? What will be the rate of return on the bond?

Solve a bond pricing problem where a bond has 10 years until maturity, an 8.1% coupon rate, and sells for $1,190. Calculate its price 1 year later with a 9.9% yield to maturity and determine the rate of return. Includes detailed calculations and financial concepts like present value and rate of return.

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