A bond with a face value of $6,000 and an annual coupon rate of 12% convertible semiannually will mature in ten years for its face value. If the bond is priced using a nominal yield rate of 6% convertible semiannually, what is the amount of premium in this bond and what is the amount for amortization of premium in the 7th coupon

Premium is $2,677.95

The premium amortization on the 7th payment is $119

Explanation:

In order to arrive at the premium on the bond,it is necessary to compute the issuing price of the bond,which can be done using the pv formula in excel as shown below:

=-pv(rate,nper,pmt,fv)

rate is the semi-annual yield to maturity on the bond which is 6%/2=3%

nper is the number of coupon interest payable by the bond,which is 10 years multiplied by 2=20

pmt is the semi-annual coupon payable by the  bond i.e 12%/2*$6000=$360

fv is the face value of the bond which is $6,000

=-pv(3%,20,360,6000)

pv=$8,677.95  

premium=issue price -face value

premium=$$8,677.95-$6,000

premium=$2,677.95

The premium amortization is the excess of coupon payment  over the interest expense.

In the attached, I calculated the premium amortization on the 7th payment.

I started by taking the issue price of $8677.95 ,added interest expense at 3% semi-annually ,deducted the coupon payment of $360,thereby leaving the outstanding balance at end of the year.

Note that the premium amortization is the excess of coupon payment over interest expense as colored coded.