Question

A thirty-year zero-coupon bond has a face value of $1,000 and a market price of $700. Face value is assumed to be $1,000.

(1) What is the yield-to-maturity on this bond?   Please type in your answer -->

Note: if you choose C, please just type C. Don't type (C) or 1.43.

   (A) 1.196%          (B) 0.7%           (C) 1.43          (D) No correct answer is given

(2) What is the (Macaulay) duration of this bond?     Please type in your answer -->

   (A) 0 year          (B) 30 years           (C) 15 years          (D) No correct answer is given

(3) What is the Modified Duration of this bond?      Please type in your answer -->

   (A) 0 year          (B) 30 years           (C) 14.84 years          (D) 29.67 years   (E) No correct answer is given

(4) If interest rate (Yield to Maturity to be more accurate) increased by 1 percentage point, what would happen to the bond price?         Please type in your answer -->  

   (A) Bond price will drop by 29.67%

(B) Bond price will rise by 29.67%

(C) Bond price will not change

(D) Bond price will drop by 30%

(E) Bond price will drop by 14.84%

   (F) No correct answer is given

Answer 1

Question 1

Yield to maturity (YTM) of a zero-coupon bond is given by;

       YTM= (F/PV)^1/n-1

Where, F is face value, PV is present value, n is period.

From the question, F= $1000, PV= $700, n= 30

Therefore,

          YTM= (1000/700)^1/30-1

                    = 0.01196

Yield to maturity= 0.0119*100= 1.196%

Correct option is: option A- 1.196%

Question 2

‘The Macaulay duration of a zero-coupon bond is equal to its maturity’.

In this question maturity is 30 years.

Therefore, the correct option is: option B – 30 Years

Question 3

The Modified Duration of a zero-coupon bond is given by;

Modified duration= Macaulay duration/ (1+YTM/2)

Therefore,

          Modified duration= 30/ (1+0.0119/2)

                                       = 29.8222

So, the correct option can be either Option E or Option D

If 29.822 is rounded to the nearest option, then the correct option is option D- 29.67 years

Otherwise, option E none of the above!