Page Enterprises has bonds on the market making annual payments, with nine years to maturity, and selling for $948. At this price, the bonds yield 5.9 percent. What must the coupon rate be on the bonds?

Coupon rate is 5.17%

Explanation:

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

Assuming Face value of the bond is $1,000

Face value = F = $1,000

Selling price = P = $948

Number of payment = n = 9 years

Bond Yield = 5.9%

The coupon rate can be calculated using following formula

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

5.9% = [ C + ( $1,000 - $948 ) / 9 ] / [ ( $1,000 + $948 ) / 2 ]

5.9% = [ C + $5.78 ] / $974

5.9% x $974 = C + $5.78

$57.466 = C + $5.78

C = $57.466 - $5.78 = $51.686

Coupon rate = $51.686 / $1,000 = 0.051686 = 5.17%

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