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.