Final answer:
To find the price of the bond at different yield rates, you can use the present value formula and the duration and convexity rules. The percent error can be calculated to evaluate the accuracy of the rules.
Step-by-step explanation:
To find the price of the bond if its yield to maturity falls to 4%, we can use the present value formula. The formula for calculating the present value of a bond is PV = C * (1 - (1 + r)^(-n)) / r + F * (1 + r)^(-n), where PV is the present value, C is the annual coupon payment, r is the yield to maturity, n is the number of periods, and F is the face value of the bond. Plugging in the values from the question, we can calculate the price of the bond.
The price predicted by the duration rule can be calculated by multiplying the duration of the bond by the change in yield and subtracting the convexity adjusted value. The duration rule is an approximation that assumes bond prices and yields move in a linear relationship.
The price predicted by the duration-with-convexity rule is calculated by adjusting the price predicted by the duration rule based on the convexity of the bond. Convexity measures the curvature of the relationship between bond prices and yields.
To calculate the percent error for each rule, we can compare the predicted prices to the actual price of the bond. The percent error is calculated by taking the absolute value of the difference between the predicted price and the actual price, dividing it by the actual price, and multiplying by 100.
The accuracy of the two rules can be evaluated based on the percent error. A smaller percent error indicates a more accurate prediction.
To find the price of the bond if its yield to maturity increases to 6%, we can use the present value formula again with the new yield rate. The price predicted by the duration rule and the duration-with-convexity rule can be calculated in the same way as before.