Answer:
In this problem, 3.8% coupon bearing bond of $1,000 each has been issued. Total 1000 bonds are issued. Each has been issued at 101.8250%. So total amount realized on issue is $1,018,250. It is the value of bond calculated at market rate. Value of a bond is the sum of the present value of cash flows. Here bond has 5 years duration. Interest is paid semiannually. So after every six month, interest payable is -
Calculate present value of 10 such semiannual payment plus principal amount payable at the end of 5th year. Add them. The amount will be current issue price of bond.
So premium amount at the time of issue is-
This premium will be amortized in 5 years period along with each semi annual interest payment is made. So on maturity, no premium amount will be left.
Here amortization will be made at effective rate. Here effective rate will mean market rate. It is 3.4% i.e. 1.7% semi annually. This effective rate is applied on carry balance of bond. Carry balance of bond is nominal value of bond plus unadjusted portion of premium.
Consider the table below. It shows calculation of effective interest rate. First effective rate is 1.7% on carry value of $1,018,250. It is $17,310. But interest actually payable is $19,000. So difference is amortized portion of premium. It is-
This amortized portion will reduce premium balance. So effective carry value of bond in the book will be
Second semiannual effective interest will be 1.7% on $1,016,560. This process will continue for 10 such semi-annual payments. Thus after 10 payments, premium account will have zero balance. Only $1,000,000 balance will appear in 3.8% bond account. It will be finally paid off by debit in 3.8% bond account and credit in cash account.
Explanation:
