Consider a $1,000 par value 20-year zero coupon bond issued at a yield to maturity of 10%.If you buy that bond when it is issued and continue to hold the bond as yields decline to 9%,the imputed interest income for the first year of that bond is

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The imputed interest income for a zero coupon bond is calculated as the difference between the purchase price and the face value of the bond at maturity. In this case, the purchase price is the issue price of the bond which is $384.62 ($1,000 / (1 + 0.1)^20), and the face value of the bond is $1,000.

When the yield declines to 9%, the price of the bond will increase to $435.60 ($1,000 / (1 + 0.09)^20). Therefore, the imputed interest income for the first year will be the difference between the purchase price and the new price, which is $50.98 ($435.60 - $384.62).

However, since this is a zero coupon bond, there is no actual interest income received over the life of the bond, only imputed interest income at maturity.

Consider a $1,000 Par Value 20-Year Zero Coupon Bond Issued