Question

1 point) Consider the continuously compounded yield curve y(T) 0.045 - 0.015e0."7. Consider a 2-year $ 1000 bond that's redeemable at par and pays semi-annual coupons at a rate of 42) 7%. (1) Determine the bond's purchase price. Purchase Price-$ (i) Determine the duration of the bond to 3 decimals. Duration Note: Use the purchase price to the closest cent in your duration calculation. years

Answer 1

(A) PURCHASE PRICE OF THE BOND

YEAR	AMOUNT	PVF @ 3.5%		PRESENT VALUE
0.5	35	0.966		33.81
1	35	0.934		32.69
1.5	35	0.902		31.57
2	35	0.871		30.485
2	1000	0.871		871
			TOTAL	999.555

HENCE, THE PURCHASE PRICE IS EQUAL TO THE FACE VALUE, i.e. $1000.

(B) DURATION OF BOND

FORMULA = [(1+Y)/Y] - [{1+Y}+PERIOD{C-Y}]/C[{1+Y}^PERIOD-1]+Y

WHERE, Y STANDS FOR YIELD TO MATURITY

C STANDS FOR COUPON RATE

IN THIS CASE, COUPON RATE AND YIELD TO MATURITY ARE SAME AS THE BOND IS GETTING REDEEMED AT PAR.

SO, SUBSTITUTING VALUES,

= (1+0.07)/0.07 - [{1+0.07} + 2{0.07-0.07}] / 0.07[{1+0.07}^2 - 1] + 0.07

= 1.93 YEARS