Question

A bond with a coupon rate of 7 percent sells at a yield to maturity of 8 percent. If the bond matures in 11 years, what is the Macaulay duration of the bond? What is the modified duration?

Answer 1

Answer:

Let us assume Par value of bond = $1000

Annual coupon = 1000 * 7% = $70

YTM = 8%

Price of bond = PV (rate, nper, pmt, fv, type)

= PV (8%, 11, -70, -1000, 0)

= $928.61

Price of bond = $928.61

Macaulay duration of the bond = 7336.04 / 928.61 = 7.90 years

Modified Duration = Macaulay duration / (1 + YTM / Number of coupon period per year) = 7.90 / (1 + 8%/1)

= 7.31 years

Hence:

Macaulay duration of the bond = 7.90 years

Modified Duration = 7.31 years