Question

A bond with 20 years to maturity is selling for $1,250 and has a yield to maturity of 7.5 percent. if this bond pays its coupon payments semi annually and its par value is $1000, what is the bonds annual coupon rate? (Round your answers two decimal places.)

A. 9.93%

B. 10.42%

C. 15.13%

D. 8.57%

Answer 1

The annual coupon rate for the Bond

The Coupon rate of the Bond is calculated using financial calculator as follows (Normally, the rate is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figures
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount	PMT	?
Market Interest Rate or Yield to maturity on the Bond [7.50% x ½]	1/Y	3.75
Maturity Period/Time to Maturity [40 Years x 2]	N	40
Bond Price/Current market price of the Bond [-$1,250]	PV	-1,250

We need to set the above figures into the financial calculator to find out the semi-annual coupon amount. After entering the above keys in the financial calculator, we get the semi-annual coupon amount (PMT) = $49.66.

Here, we get semi-annual Coupon amount = $49.66.

Therefore, the Annual Coupon Amount = $99.33 [$49.66 X 2]

The coupon rate is calculated by dividing the annual coupon amount with the par value of the Bond

So, Annual Coupon Rate = [Annual Coupon Amount / Par Value] x 100

= [$99.33 / $1,000] x 100

= 9.93%

Hence, the bonds annual coupon rate will be (A). 9.93%