Laurel inc and Hardy corp both have 10 percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $1,000. The Laurel, Inc., bond has five years to maturity, whereas the Hardy Corp. bond has 16 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? If the interest rates fall by 2 percent?

current bond price $1,000

interest rate 10%

Laurel bond matures in 5 years, 10 semiannual payments

Hardy bonds matures in 16 years, 32 semiannual payments

if market interest increases to 12%

Laurel bond:

$1,000 / (1 + 6%)¹⁰ = $558.39

$50 x 7.36009 (annuity factor, 6%, 10 periods) = $368.00

market price = $926.39

% change = -7.36%

Hardy bond:

$1,000 / (1 + 6%)³² = $154.96

$50 x 14.08404 (annuity factor, 6%, 32 periods) = $704.20

market price = $859.16

% change = -14.08%

current bond price $1,000

interest rate 10%

Laurel bond matures in 5 years, 10 semiannual payments

Hardy bonds matures in 16 years, 32 semiannual payments

if market interest decreases to 8%

Laurel bond:

$1,000 / (1 + 4%)¹⁰ = $675.56

$50 x 8.1109 (annuity factor, 4%, 10 periods) = $405.55

market price = $1,081.11

% change = 8.11%

Hardy bond:

$1,000 / (1 + 4%)³² = $285.06

$50 x 14.08404 (annuity factor, 4%, 32 periods) = $704.20

market price = $1,178.74

% change = 17.87%

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