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19 February, 17:28

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.

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  1. 19 February, 17:54
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    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
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