Abriele Enterprises has bonds on the market making annual payments, with 19 years to maturity, a par value of $1,000, and selling for $910. At this price, the bonds yield 7.8 percent. What must the coupon rate be on the bon

The coupon rate on the bond must be 6.98%

Explanation:

Yield to maturity is the annual rate of return that an investor receives if a bond bond is held until the maturity.

Face value = F = $1,000

Selling price = P = $910

Number of payment = n = 19 years

Bond Yield = 7.8%

The coupon rate can be calculated using following formula

Yield to maturity = [ C + ( F - P ) / n ] / [ (F + P ) / 2 ]

7.8% = [ C + ( $1,000 - $910 ) / 19 ] / [ ( $1,000 + $910 ) / 2 ]

7.8% = [ C + $4.74 ] / $955

7.8% x $955 = C + $4.74

$74.49 = C + $4.74

C = $74.49 - $4.74 = $69.75

Coupon rate = 69.75$ / $1,000 = 0.06975 = 6.975%

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