252

NATURE OF CAPITAL AND INCOME

        

[Cuar. XIV

 
 
 
 
 
 

to pay an annually increasing tax on this saving for the 14
years of postponement, and then a tax on the income from
these same savings in which his annuity is to consist.
His first year’s savings will be $500 and will be taxed $50.
During the second year his capital grows from $10,500 to
$11,025, making an increase of $525, the tax on which is
$52.50, and so on, as shown in the preceding table.

 
 
 
 
 
   
   
 
   
  
  

 

The third brother, under such a tax, will fare as shown

 

 

 

 

 

 

 

below : —
TaIRD BROTHER
SO-CALLED TAX | TrUE TAX
CAPITAL |iyxcomE”| THEREON | INCOME |THEREON
At beginning $10,000
In 1 year 8,500 $500 $50.00 | $2,000 | $200
In 2 years 6,930 425 42.50 2,000 200
In 3 years 5,270 340 34.00 2,000 200
In 4 years 3,530 260 26.00 2,000 200
In 5 years 1,710 180 18.00 2,000 200
In 6 years nil 90 9.00 1,800 180
Thereafter nil nil nil ail nil
|

 

 
 
 
 
 
 
 
 
 
 
 
  
 
   

 

 

When we compare the burden of the various taxes imposed
 on so-called “income,” we shall find that the first
brother could “compound” for his taxes, as before, by a
cash payment of $1000. The second brother, however,
would need to pay $1714. For he would have to pay $1000
as the present value of the tax of $100 a year beginning in
14 years, and in addition, $714 as the present value of
the series of taxes on his savings, namely, $50, $52.50, ete.
And the third brother, though the least provident of all,
could compound for only $157.73, this being the present
value of the six small tax payments which he would have
to make, namely, $50, $42.50, $34, $26, $18, and $9.
1 In the foregoing calculation it was assumed that the tax did not
itself affect the value of the “income” on which the tax is laid. But
this would be untrue of ‘income’ which includes the increment of
capital. For the discussion of this point, see Appendix to Chap.
XIV, § 2.