Hi I am having difficulty with the question posted below. Specifically, I am having issues with C and D of this question. For part B of this question I got 3.95 as the duration and the YTM as 11.8116%. Lastly, how does one calculate YTM to EAR. For example if I wanted to know 10YTM is equal to what EAR, what formula does one use? Thank you for your help in this matter, it is greatly appreciated.

B).Calculate the duration of a coupon bond with the following features. What general conclusion can we make about the duration of coupon bonds relative to their time to maturity?(3 marks)

Face value of $1000

Five years to maturity

Coupon rate of 11%, paid semi-annually

Current price of $970

(Hint: The effective annual yield should be 12.1604%.)

C)Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bond's price by 5 * 0.1% = 0.5%, approximately.

Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a "parallel upward shift in yields of 10 basis points"). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price are inversely related to each other (i.e., an increase in yield should lead to a decrease in bond price).(2 marks)

D) Recalculate the price of the coupon bond with five years to maturity, face value of $1000, coupon rate of 11% paid semi-annually, and a new yield to maturity equaling the original yield in part (b) plus 0.1%. Does it concur with your approximate coupon bond price calculated in part (c)? (Hint: The two answers in parts (c) and (d) should be fairly similar.)