Question

(1 point) Consider the continuously compounded yield curve y(T-0.035-0.0 15є-0.5T Consider a 2-year $ 2500 bond that's redeemable at par and pays semi-annual coupons at a rate of C(2) 596. () Determine the bond's purchase price. Purchase Price $ (i) Determine the duration of the bond to 3 decimals. Duration years Note: Use the purchase price to the closest cent in your duration calculation

Answer 1

(I) The solution is

Bond Payouts	Time, t	Y(t)	1+Y(t)	Discount Factor	Present Value
(1) = Coupon Rate * Bond Price + Bond Price (at t=2)	(2)	(3) = 0.035-0.015*EXP(-0.5*(2))	(4) = 1+(3)	(5) = 1/(4)	(6) = (1) * (5)
0	0	0.02	1.020	0.980392157	0.00
125	0.5	0.02	1.023	0.977213351	122.15
125	1	0.03	1.026	0.974751936	121.84
125	1.5	0.03	1.028	0.972843557	121.61
2625	2	0.03	1.029	0.971362478	2549.83
SUM					2915.43

Therefore, the purchase price is 2915.43

(II)

Time, t	Present Value	Weighted Present Value
(1)	(2) (from table above)	(3) = (1) * (2)
0	0.00	0.00
0.5	122.15	61.08
1	121.84	121.84
1.5	121.61	182.41
2	2549.83	5099.65
SUM	2915.43	5464.98

Duration = Weighted Price Value / Current Market Value = 5464.98/2915.43 = 1.875