Question

find with formulas

Modified Duration:

         For this bond:    coupon interest rate: 5%. yield: 4%; semiannual pay; 2 years.

         a.      find the bond price in decimal format (as though principal is 1.0) and in percentage-of- par format.

         b.      using that price find the Macauley Duration.

         c.      using Macauley Duration find Modified Duration

Answer 1

Price of bond = Interest*PVAF at 2% for 4 semiannual period + face value*PVF at 2% for 4th semiannual period

.025* 3.8977 + 1*.9238 = 1.019

Price as % of par = (1.019/1)*100 = 101.9039

PVAF at 2% = 1-(1+r)^-n/r = 1-(1.02)^-4 /.02 =3.8077

PVF at 2% for 4th semiannual period = 1/(1+r)^n = 1.(1.02)^4 = .9238

b-

semiannual period	cash flow	present value of cash flow =cash flow/(1+r)^n r= 2%	present value* semiannual period
1	0.025	0.02451	0.02451
2	0.025	0.024029	0.048058
3	0.025	0.023558	0.070674
4	1.025	0.946942	3.787766
total			3.931009
Macculays duration in years	total/market price	3.9310/1.019	3.857704
Modified duration	maculays duration/(1+YTM/n)	3.8577/(1.02)	3.782059