Question

You have just purchased a 15 year, ​$1,000 par value US Government bond for​ $909.20. The yield to maturity on the bond is​ 8.6%. What is the coupon​ rate?

A. ​9.0% B. ​7.0% C. ​8.6% D. ​7.5% E. ​15.0%

Answer 1

Calculation of Annual Coupon Rate of the Bond

Par Value = $1,000

Bond Price = $909.20

Annual Yield to Maturity = 8.60%

Maturity Years = 15 Years

Let’s take “C” as the annual coupon amount

The Current Price of the bond = Present Value of the semiannual coupon amounts + Present Value of the Par Value

$909.20 = C[PVIFA 8.60%, 15 Years] + $1,000[PVIF 8.60%, 15 Years]

$909.20 = [C x 8.25461] + [$1,000 x 0.29010]

$909.20 = [C x 8.25461] + $290.10

[C x 8.25461] = $909.20 - $290.10

[C x 8.25461] = $619.10

C = $619.10 / 8.25461

C = $75.00

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

= [$75.00 / $1,000] x 100

= 7.50%

“Therefore, the Coupon Rate of the Bond will be (D). 7.5%”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.