APPENDIX TO CHAPTER XIV 
  
399 
¢—a. As the rate is, the tax is (¢c—#)t. The discounted value 
of this tax is c—o)t This deducted from the discounted 
value, iy of next year’s capital-value is this year’s capital- 
value, z; i.e, — PO A, a. 
ivi 1+ 
Solving for z, we have, a= Lan 
1—t+417 
The tax itself is #(¢ — =), which, if we substitute for its value 
cit 
1-741 
If we substitute for ¢ and ¢ their assumed values, .05 and .10, 
we have =e X .J947 
and tax = ¢ x .0053. 
Substituting for ¢ its value at the end of the fifteenth year, 
namely, $18,000, we find that , the value one year earlier, 
will be 18,000 x .957, or $17,046, and that the value one year 
previous will be the latter sum multiplied likewise by .947, or 
$16,142.56, and so on until the present is reached, when the 
value will be $7,952.15. The table below will show, there- 
fore, the total effect of a 109, tax on the increase of value, 
just found, reduces to 
  
  
  
  
  
  
  
CAPITAL-VALUE INCREASE Oe Carma "| 109 Tax TaEREON 
Beginning $ 7,952.16 enn “iwi 
End of 1year 8,397.20 $445.06 $44.51 
End of 2 years 8,867.27 470.07 47.01 
End of 3years 9,363.54 496.27 49.63 
End of 4 years 9,887.58 524.04 52.40 
End of 5years 10,440.95 553.37 55.34 
End of 6 years 11,025.29 584.34 58.43 
End of 7 years 11,642.33 617.04 61.70 
End of 8years 12,293.91 651.58 65.16 
End of 9years 12,982.06 688.15 68.82 
End of 10 years 18,708.62 726.56 72.66 
End of 11 years 14,475.84 767.22 76.72 
End of 12 years 15,286.00 810.16 81.02 
End of 13 years 16,142.56 856.56 85.66 
End of 14 years 17,046.00 903.44 90.34 
End of 15 years 18,000.00 954.00 95.40