A 10-year $1,000 bond pays a nominal rate of 9% compounded semi-annually. If the market interest rate is 12% compounded annually and the general inflation rate is 6% per year, find the actual-and constant-dollar amounts (in time-0 dollars) of the 15th interest payment on the bond.

a) actual dollar = $60

b) Constant dollar of the 15th payment = $38.710

Explanation:

Facts from the question:

The Face value of the bond = $1,000

Nominal Interest rate = 12% and it compounded annually

General inflation rate = 6%

The question: Determine the 15th interest payment on the bond.

Step 1: The coupon for the amount of semi annual payment is as follows:

Coupon = (Interest rate / Number of compounding times in a year) x face value of the bond

= (0.12/2) x 1000

= $60 - = Actual dollar amount

Step 2: Determine the 15th payment and this will represent the middle of the 8th year or (7 1/2) year.

To calculate this=

Constant dollar amount of the 15th interest payment

= Actual dollar amount (above) / (1 + inflation rate) ∧n

where n = the number of years = 7.5 years

= $60 / (1 + 0.06) ∧7.5

= $60/1.55

= $38.710

This means the constant dollar amount on that 15th payment = $38.710