Question

A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of 5.5% 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. (Round your answers to 2 decimal places.)

Answer 1

Answer:

imputed interest income for first year is $18.85

imputed interest income for second year is $19.89

imputed interest income for last year is $52.14

Explanation:

given data

maturity time = 20 year

yield to maturity = 5.5%

face value $1,000

solution

first we get here constant yield for year 0 , 1 , 2 , 19, 20

constant yield = $\frac{face\ value}{(1+r)^t}$    ............1

constant yield for year 0 so maturity time = 20

constant yield for year 0 = $\frac{1000}{(1+0.055)^{20}}$ = 342.72

constant yield for year 1 = $\frac{1000}{(1+0.055)^{19}}$ = 361.57

constant yield for year 2 = $\frac{1000}{(1+0.055)^{18}}$ = 381.46

constant yield for year 19 = $\frac{1000}{(1+0.055)^{1}}$ = 947.86

constant yield for year 20 = $\frac{1000}{(1+0.055)^{0}}$  = 1000

so  imputed interest income for first year is =  361.57 -  342.72 = $18.85

and imputed interest income for second year is = 381.46 - 361.57  = $19.89

and imputed interest income for last year is = 1000 - 947.86 = $52.14