A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of 8% and face value $1,000. Find the imputed interest income in: (a) the first year; (b) the second year; and (c) the last year of the bond’s life.

First Year$ 17.17

Second Year$ 18.53

Last Year$ 74.08

Explanation:

Computation to Find the imputed interest income in: (a) the first year; (b) the second year; and (c) the last year of the bond’s life

Imputed Interest

First step

Using this formula

Imputed interest=(Present Value /1+Yield to maturity)^Numberd of years

YearYears Remaining to MaturityConstant Yield Value ( 1 / 1.08)^n

020(1/1.08)^20= $ 214.54

119(1/1.08)^19=$ 231.71

218(1/1.08)^18=$ 250.24

191(1/1.08)^1=$ 925.92

200(1/1.08)^0=$ 1,000

Second step is to find the Imputed interest for the first year, second year; and the last year of the bond’s life

YearYears Remaining to MaturityConstant Yield Value ( 1 / 1.08)^n=Imputed Interest

020 $ 214.54

119$ 231.71 $17.17

($231.71-$214.54)= $17.17

218$ 250.24 $18.53

($250.24-$231.71)=$18.53

191$ 925.92

200$ 1,000$74.08

($1,000-$925.92) =$74.08

Therefore the imputed interest will be:

First Year$ 17.17

Second Year$ 18.53

Last Year$ 74.08

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