Question

A 10-year, 7 percent coupon bond pays interest semiannually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 6 percent from the current rate of 5.5 percent?

Answer #1

**PERCENTAGE DECREASE IN PRICE = 3.57%**

PRICE OF BOND = C x (1- (1 +r)^{-n} / r) + F /
(1+r)^{n}

COUPON (C) = 1000 x 7% = 70/2 = 35

YTM (r) = 5.5%/ 2 = 2.75%

MATURITY (n) = 10x 2 = 20

FACE VALUE (F) = 1000

PRICE OF BOND = 35 x (1- (1 +0.0275)^{-20} / 0.0275) +
1000 / (1+0.0275)^{20}

= 1,114.2

**WHEN YTM RISES TO 6%**

PRICE OF BOND = C x (1- (1 +r)^{-n} / r) + F /
(1+r)^{n}

COUPON (C) = 1000 x 7% = 70/2 = 35

YTM (r) = 6%/ 2 = 3%

MATURITY (n) = 10x 2 = 20

FACE VALUE (F) = 1000

PRICE OF BOND = 35 x (1- (1 +0.03)^{-20} / 0.03) + 1000
/ (1+0.03)^{20}

= 1,074.39

PERCENTAGE DECREASE IN PRICE = 1,114.20 - 1,074.39 / 1,114.2

= - 3.57%

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