Question

what is the coupon rate for a $2,000 face value bond with annual coupon payments, current price of $3,000, yield to maturity of 5.15%, and 12 years to maturity?

Answer 1

Given,

Face value = $2000

Current price = $3000

Years to maturity (n) = 12 years

Yield to maturity (r) = 5.15% or 0.0515

Solution :-

Let coupon payment be 'C'

Current price = C/r x [1 - (1 + r)^-n] + [Face value (1 + r)ⁿ]

$3000 = C/0.0515 x [1 - (1 + 0.0515)^-12] + [$2000 (1 + 0.0515)¹²]

$3000 = C/0.0515 x [1 - (1.0515)^-12] + [$2000 (1.0515)¹²]

$3000 = C/0.0515 x [1 - 0.5473796855] + [$2000 1.8268854808]

$3000 = C/0.0515 x [0.4526203145] + [$1094.75937108]

$3000 - $1094.75937108 = C/0.0515 x 0.4526203145

$1905.24062892 = C/0.0515 x 0.4526203145

($1905.24062892 x 0.0515) 0.4526203145 = C

$216.7819 = C

Now,

Coupon rate = C face value

= $216.7819 $2000 = 0.10839 or 10.839%