Question

Big Pear has 10,000 outstanding bonds. These bonds have a 30-year maturity and $1,000 par value. Their yield to maturity is 8%, they pay interest semiannually, and they sell at a price of $1,113.12. What is the bond's coupon interest rate?

	6%
	7%
	8%
	9%
	10%
	4.5%

Answer 1

Solution :-

Semiannual Yield to Maturity = 8% / 2 = 4%

Time to Maturity of Bond = 30 Years

Semiannual Period = 30 * 2 = 60

Face Value of Bond = $1,000

Price of Bond = $1,113.12

Now Assume Semiannual Coupon Payment = X

Now $1,113.12 = X * PVAF( 4% , 60 ) + $1,000 * PVF ( 4% , 60 )

= $1,113.12 = ( X * 22.6235 ) + ( $1,000 * 0.09506 )

= $1,113.12 =  ( X * 22.6235 ) + $95.06

Now ( X * 22.6235 ) = $1,018.06

X = $45

Therefore Semiannual Coupon Rate = $45 / $1,000 = 4.5%

Annual Coupon Rate = 4.5% * 2 = 9.00%

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