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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Since it is a zero-coupon bond, there are no coupon payments during the life of the bond. Therefore, the imputed interest income is the difference between the purchase price of the bond and its face value at maturity. At a yield to maturity of 10%, the purchase price of the bond would be:

PV = FV / (1 + r)^n
PV = 1,000 / (1 + 0.10)^20
PV = $148.64

At a yield to maturity of 9%, the price of the bond would be:

PV = FV / (1 + r)^n
PV = 1,000 / (1 + 0.09)^20
PV = $182.67

Therefore, the imputed interest income for the first year would be the difference between the purchase price and the face value at maturity, divided by the number of years to maturity:

Imputed interest income = (FV - PV) / n
Imputed interest income = (1,000 - 148.64) / 20
Imputed interest income = $42.07 / year

However, we are only interested in the imputed interest income for the first year, so we need to adjust this amount for one year of holding period. The imputed interest income for the first year would be:

Imputed interest income = ($182.67 - $148.64) / 20
Imputed interest income = $1.80 per year

And finally, we need to calculate the present value of this imputed interest income for one year at a yield to maturity of 9%:

PV = C / (1 + r)^n
PV = $1.80 / (1 + 0.09)^1
PV = $1.65

Therefore, the imputed interest income for the first year of holding the bond would be $1.65. The closest answer choice is B) $14.87, which is the present value of the total imputed interest income for the remaining 19 years of holding the bond at a yield to maturity of 9%.

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