A 30-year maturity bond making annual coupon payments with a coupon rate of 8.5% has duration of 12.88 years and convexity of 235.95. The bond currently sells at a yield to maturity of 7%. a. Find the price of the bond if its yield to maturity falls to 6%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Price of the bond b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Predicted new price (duration rule) c. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

a. Predicted Price = $1815.52

b. Predicted Price = $1,834.64

c. Predicted Price = $1425.4

Explanation:

The actual price of the bond as a function of yield to maturity is:

Yield to maturity --- Price

7% $1,620.45

8% $1,450.31

9% $1,308.21

a.

Using the Duration Rule, assuming yield to maturity falls to 6%:

Predicted price change = (-D/(1 + y)) * ∆y * Po

Where D = Duration = 12.88 years

y = YTM = 7%

∆y = 6% - 7% = -1%

Po = $1,620.45

So, Predicted Change = (-12.88/(1 + 0.07)) * -0.01 * 1,620.45

Predicted Change = 195.0597757009345

Predicted Change = $195.06 Approximated

Therefore the new Predicted Price

= $1,620.46 + $195.06

= $1815.52

b.

Using Duration-with-Convexity Rule, assuming yield to maturity falls to 6%

Predicted price change

= [(-12.88/(1 + 0.07)) * (-0.01) + (½ * 235.95 * (-0.01²))] * 1,620.45

= 214.1770345759345

= $214.18 Approximated

Therefore the new Predicted Price

= $1,620.46 + $214.18

= $1,834.64

c.

Using the Duration Rule, assuming yield to maturity rise to 8%:

Predicted price change = (-D/(1 + y)) * ∆y * Po

Where D = Duration = 12.88 years

y = YTM = 7%

∆y = 8% - 7% = 1%

Po = $1,620.45

So, Predicted Change = (-12.88/(1 + 0.07)) * 0.01 * 1,620.45

Predicted Change = -195.0597757009345

Predicted Change = -$195.06 Approximated

Therefore the new Predicted Price

= $1,620.46 - $195.06

= $1425.4

im confused need to go into details plz thx