The U.S. Government has a 24-year bond that matures 24 years from now and has a
ID: 2737758 • Letter: T
Question
The U.S. Government has a 24-year bond that matures 24 years from now and has a face value of $1,000 . The bond has a coupon rate of 3.1% per year, paid semiannually. The yield on the bond is 7%. If coupons are reinvested at 3.6% per annum, then how much interest is earned on reinvested coupons over the life of the bond? Calculate the interest as a percentage of the total cash flows received by the bondholder.
What is the amount of interest earned on reinvesting the coupons? $_________(Round to the nearest cent.)
Explanation / Answer
Interest earned on reinvested couon is => FV of Coupon - Coupons Recieved
PMT => (1000 *3.1%)*/2 => 15.5
interest => 3.6/2 => 1.8%
N => 24 *2 =>48
PV => 0
FV => PMT [( 1 + Interest)n -1 / Intrerest)]
=> 15.5 [ ( 1 + 1.80%)48 -1 / 1.80%]
=> $1162.5
Interest earned on reinvested couon is => 1162.5 - (15.5 * 48)
The amount of interest earned on reinvesting the coupons=> $418.5
As a percentage of the total cash flows from the bond (coupon income + principal),
the interest as a percentage of the total cash flows received by the bondholder. => 418.5 / ( 1000 + 1162.5)
The interest as a percentage of the total cash flows received by the bondholder => 19.35%
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