A $7,000 bond with a coupon rate of 6.7% paid semi-annually has 5 years to maturity and a yield to maturity of 6.1% p.a., compounded semi-annually. If interest rates fall and the yield to maturity decreases by 0.6%, the price of the bond would expected to increase by how much in dollar value? (Round your answer in dollars to 2 decimal places

We can solve this problem using the bond pricing formula, considering the changes in yield to maturity (YTM). Here are the steps:

### Step 1: Bond price formula

The price of a bond can be calculated using the formula:

\[
P = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) + F \times (1 + r)^{-n}
\]

Where:
- $ P $ is the price of the bond.
- $ C $ is the semi-annual coupon payment, which is calculated as $ C = \frac{\text{Coupon rate} \times \text{Face value}}{2} $.
- $ F $ is the face value of the bond (here, $7,000).
- $ r $ is the semi-annual yield to maturity, calculated as $ \frac{\text{Annual YTM}}{2} $.
- $ n $ is the total number of periods (here, $ 5 \times 2 = 10 $ since the bond matures in 5 years and the payments are semi-annual).

### Step 2: Initial Bond Price Calculation (Before Interest Rate Decrease)

- Face Value $ F = 7,000 $.
- Annual Coupon Rate = 6.7% implies semi-annual coupon rate = 6.7% / 2 = 3.35%.
- Coupon payment $ C = \frac{6.7\% \times 7,000}{2} = 234.5 $.
- Yield to maturity (YTM) = 6.1% per annum compounded semi-annually, implying semi-annual yield $ r = \frac{6.1\%}{2} = 0.0305 $.

Now, calculate the bond price with this yield.

### Step 3: New Bond Price Calculation (After Interest Rate Decrease)

The new yield to maturity after a 0.6% decrease becomes $ 6.1\% - 0.6\% = 5.5\% $, which implies a semi-annual yield $ r_{\text{new}} = \frac{5.5\%}{2} = 0.0275 $.

Now, calculate the new bond price with this adjusted yield.

### Step 4: Calculate the Price Change

The price increase is the difference between the new price (after the yield drop) and the original price. Let's calculate these prices.The initial price of the bond is \$7,178.68, and after the interest rate decreases, the new price is \$7,362.88. Therefore, the price of the bond increases by \$184.21.

Would you like more details or have any further questions?

Here are some related questions:
1. How is the yield to maturity (YTM) calculated for bonds?
2. What happens to bond prices when interest rates rise?
3. What is the difference between current yield and YTM?
4. How do coupon bonds differ from zero-coupon bonds?
5. Why are bond prices and yields inversely related?

**Tip:** The longer the bond's maturity, the more sensitive its price is to interest rate changes.

A $7,000 bond with a coupon rate of 6.7% paid semi-annually has 5 years to maturity and a yield to maturity of 6.1% p.a., compounded semi-annually. If interest rates fall and the yield to maturity decreases by 0.6%, the price of the bond would expected to increase by how much in dollar value? (Round your answer in dollars to 2 decimal places)

Learn how to calculate the price increase of a $7,000 bond when the yield to maturity decreases by 0.6%. This problem explores bond pricing, interest rate sensitivity, and uses key finance formulas like the bond price formula. Suitable for college-level finance or economics students.

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