Question

6. What is the duration of a two-year bond that pays an annual coupon of 5%, returns the face value, and has a current yield to maturity of 4.5%. Use $1000 as the face value. (show the calculation, so i can study)

7. What is the duration of a two-year zero-coupon (principal-only) bond that is yielding 6% and $10,000 face value? Note: This bond does not have coupon payments but does return the face value. (show the calculation, so i can study)

Answer 1

6. What is the duration of a two-year bond that pays an annual coupon of 5%, returns the face value, and has a current yield to maturity of 4.5%. Use $1000 as the face value.

We have the following information

Face value or maturity value M = $1000

Coupon rate = 5% per annum, therefore C = 5% of $1000 = $50

Maturity time = 2 years, therefore n = 2

Yield to maturity i = 4.5% per annum

Duration calculation:

Year (t)	Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) of CF discounted at 4.5% [PV=CF/(1+4.5%)^t]	PV *t
1	$50.0	$47.85	$47.85
2	$50.0	$45.79	$91.57
2	$1,000.0	$915.73	$1,831.46
Sum		$1,009.36	$1,970.88
		Bond's Price?
	Duration = Sum of (PV*t)/Bond's Price =	$1,970.88/$1,009.36	1.95	Years

Therefore Duration is 1.95 years (for a coupon paying bond, duration is always less than its maturity period)

7. What is the duration of a two-year zero-coupon (principal-only) bond that is yielding 6% and $10,000 face value?  

Duration for zero coupon bonds is equal to its maturity time as its all cash flow occurs at the time of maturity. Therefore the duration of a two-year zero-coupon bond is 2 years.