Question

Suppose you purchase a zero coupon bond with face value $1,000, maturing in 27 years, for $693.33. What is the implicit interest, in dollars, in the first year of the bond's life?

Answer 1

Solution:

Calculation of implicit interest rate in a zero coupon bond :

The interest rate implicit rate in a zero coupon bond can be calculated using the following formula

Interest rate = r = [ ( Face value / Purchase Price )( 1 / Years to maturity ) ] - 1

As per the Information given in the question we have

Face value of the bond = $ 1,000    ;    Purchase price of the bond = $ 693.33    ;

Years to maturity = 27 years

Applying the above values in the formula we have

= [ ( 1000 / 693.33 ) ( 1/ 27) ] – 1

= [ ( 1000 / 693.33 ) ( 0.037037 ) ] – 1

= [ (1.442315) ( 0.037037 ) ] – 1

= 1.013657 – 1

= 0.013657

= 1.3657 %

Thus the Interest rate Implicit in the zero coupon bond = 1.3657 %      

Note : ( 1.442315 ) ( 0.037037 ) = 1.013657 is calculated using the excel formula =POWER(Number,Power) =POWER(1.442315,0.037037)

Calculation of implicit interest, in dollars, in the first year of the bond's life :

The formula for calculating the implicit interest, in dollars, in the first year of the bond's life

= Purchase price of the bond * Implicit interest rate

As per the information available we have

Purchase price of the bond = $ 693.33 ;   Implicit interest rate = 1.3657 %

Applying the above information in the formula we have

= $ 693.33 * 1.3657 %

= $ 9.468950

= $ 9.4689 ( when rounded off to four decimal places )

Thus the implicit interest, in dollars, in the first year of the bond's life = $ 9.4689

= $ 9.47 ( when rounded off to two decimal places )