Question

A bond with 7 years left to maturity is trading for $967. It pays coupons semiannually. Its YTM is currently 3.6%. The coupon rate for this bond must be ________%. Do not round any intermediate work. Round your *final* answer to 2 decimal places (example: .1234567 = 12.35). Do not enter the % sign. Margin of error for correct responses: +/- .03%.

Answer 1

Face value of the bond = $1000

Current price of the bond = $967

YTM = 3.6%

Time to maturity in years = 7

The bond pays coupons semiannually. Hence we will consider semi-annual YTM and time to maturity in semiannual periods.

Semi-annual YTM = 3.6%/2 = 1.8%

Time to maturity in semiannual periods = 7*2 = 14

Semi-annual coupon payment calculation using ba ii plus calculator

We can calculate the coupon payment using ba ii plus calculator as shown below:

Input the following values in ba ii plus calculator

N = 14

I/Y = 1.8

PV = -967

FV = 1000

CPT -> PMT [Press CPT and then press PMT]

We get, PMT = 15.3123557

Note this is the semiannual coupon payment and we can convert into annual coupon by multiplying it by 2.

Annual coupon payment = 15.3123557*2 = 30.62471141

Annual coupon rate = Annual coupon payment/Face value = 30.62471141/1000 = 3.062471141%

Annual coupon rate = 3.062471141% ~ 3.06% (Rounded to two decimals)

Answer (%) -> 3.06