The formula to calculate price of a zero coupon bond is:

Price of zero coupon bond= Par value/ (1+ interest rate)^ time till maturity

Par value= 1000

Interest rate =11%

Time till maturity= 25

So,

 

= 1000/ (1+ 11%)^ 25

=  $73.61

 

Interest rate falls= 9%

 Price of zero coupon bond= Par value/ (1+ interest rate)^ time till maturity

= 1000/ (1+ 9%)^ 24

=    $ 126.40 

 

Capital gain= $ 126.40 - $73.61

= $52.79

 

The formula to calculate price of a coupon bond is:

Price= C*[(1- (1+ r)^ -n)/ r]+ Par value/ (1+ r)^ n

here,

C= coupon payment

r= Interest rate

n= Time till maturity

 

So,

At present using an interest rate of 11%, price of this bond is:

Price= (1000* 9.5%)* [(1- (1+ 11%)^ -20)/ 11%]+ 1000/ (1+ 11%)^ 20

= 95* 7.96333+ 124.0339

=  $ 880.55 

 

Now, when after one year, interest rates drop to 9%, the price of this bond becomes:

Price= (1000* 9.5%)* [(1- (1+ 9%)^ -19)/ 9%]+ 1000/ (1+ 9%)^ 19

= 95* 8.95011+ 194.4897

=    $1,044.75 

 

Capital gain= 1044.75- 880.55

=  $164.20 

 

Now, in terms of dollar return, 9.5% bond provides a higher capital gain but a better way is to look at percentage returns which is more in the case of zero coupon bond.

Even if an income of $95 is added to calculate the total return, in percentage terms, zero coupon bond still provides a better return. Percentage return from zero coupon bond is 71.72% (52.79/ 73.61). Percentage return from 9.5% bond is 29.44%(($164.20  + 95)/  $ 880.55 )

One issue provides better returns than the other because of varying interest rate sensitivity. Different bonds show different price sensitivity towards interest rate fluctuations. In general higher a bond's maturity and lower its coupon rate, higher is the price sensitivity in percentage terms.

Out of the two bonds zero coupon bond has a higher duration and therefore, should be more price volatile.