Difference between revisions of "Example:Amortized loan calculator"
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== Theory and background == | == Theory and background == | ||
Revision as of 17:59, 7 October 2008
| Amortized loan calculator | |
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| author | Leif Roschier |
|---|---|
| File:Amortized load.pdf | |
Contents
Theory and background
This approach of constructing an amortized loan calculator is similar to one in Ref. [1]
Equation for amortized loan [2] is:
[math] \frac{a}{A} = \frac{\frac{p}{100\times 12}}{1-\frac{1}{(1-\frac{p}{100\times 12})^{12n}}}, [/math]
where [math]A[/math] is the amount of loan, [math]a[/math] is monthly payment amount, [math]p[/math] interest rate per year (monthly interest rate is taken as [math]p/12[/math])[3] and [math]n[/math] is number of years for payment.
This equation of four variables is probably impossible to present with line and grid nomographs. For this reason a "Type 5" contour nomogram is constructed of the right hand side of the equation and left hand equation is just N-nomogram (Type 2). The two equations for nomogram construction are:
[math] x = \frac{a}{A} [/math]
and
[math] x = \frac{\frac{p}{100\times 12}}{1-\frac{1}{(1-\frac{p}{100\times 12})^{12n}}}. [/math]
In practice [math]x[/math] is the x-coordinate of the canvas where nomogram is constructed.
Right hand side of equation
By defining coordinates [math]x\,[/math] and [math]y\,[/math]:
[math] x = \frac{\frac{p}{100\times 12}}{1-\frac{1}{(1-\frac{p}{100\times 12})^{12n}}}, [/math]
[math] y = 12n, \, [/math] we may solve [math]y\,[/math] in terms of [math]x\,[/math] and [math]n\,[/math]:
[math] y = \frac{\log (\frac{x}{x-\frac{p}{100\times 12}})}{\log (1+\frac{p}{100 \times 12})} \, [/math]
The previous two equations are of correct form
[math] y = f_1(v) \, [/math]
and
[math] y = f_2(x,u) \, [/math]
for type 5 nomogram. For compressing time axis ([math]y[/math]-axis), we transform [math]y \rightarrow \log y [/math] and find
[math] y = \log \left( \frac{\log (\frac{x}{x-\frac{p}{100\times 12}})}{\log (1+\frac{p}{100 \times 12})} \right)\, [/math]
[math] y = \log( 12n ). \, [/math]
Left hand side of equation
Left hand side of equation
[math] x = \frac{a}{A} [/math]
is just N-nomogram
[math] F_1(u_1) = F_2(u_2)F_3(u_3) \, [/math]
References
- ↑ d'Ocagne: Traite nomographie, 1899
- ↑ http://en.wikipedia.org/w/index.php?title=Amortization_calculator&oldid=220083943
- ↑ http://en.wikipedia.org/wiki/Annual_percentage_rate#Does_not_represent_the_total_cost_of_borrowing
Generated nomograph
| Amortized loan calculator | |
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| Generated portable document file (pdf): | amortized_loan.pdf |
Source code
""" ex_amortized_loan.py Amortized loan calculator Copyright (C) 2007-2008 Leif Roschier This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. """ from nomographer import * # Type 5 grid def f1(x,u): return log(log(x/(x-u/(100.0*12.0)))/log(1+u/(100.0*12.0))) block_1_params={ 'width':10.0, 'height':5.0, 'block_type':'type_5', 'u_func':lambda u:log(u*12.0), 'v_func':f1, 'u_values':[10.0,15.0,20.0,25.0,30.0,40.0,50.0,60.0], 'v_values':[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0], 'wd_tag':'A', 'u_title':'years', 'v_title':r'interest rate \%', } # this is non-obvious trick to find bottom edge coordinates of the grid in order # to align it with N nomogram block1_dummy=Nomo_Block_Type_5(mirror_x=False) block1_dummy.define_block(block_1_params) block1_dummy.set_block() # Let's define the N-nomogram N_params_3={ 'u_min':block1_dummy.grid_box.params_wd['u_min'], 'u_max':block1_dummy.grid_box.params_wd['u_max'], 'function':lambda u:u, 'title':'', 'tag':'A', 'tick_side':'right', 'tick_levels':2, 'tick_text_levels':2, 'reference':False, 'tick_levels':0, 'tick_text_levels':0, 'title_draw_center':True } N_params_2={ 'u_min':30.0, 'u_max':1000.0, 'function':lambda u:u, 'title':'Loan', 'tag':'none', 'tick_side':'left', 'tick_levels':3, 'tick_text_levels':2, 'title_draw_center':True } N_params_1={ 'u_min':0.2, 'u_max':3.0, 'function':lambda u:u, 'title':'monthly payment', 'tag':'none', 'tick_side':'right', 'tick_levels':3, 'tick_text_levels':2, 'title_draw_center':True } block_2_params={ 'block_type':'type_2', 'width':10.0, 'height':20.0, 'f1_params':N_params_1, 'f2_params':N_params_2, 'f3_params':N_params_3, } main_params={ 'filename':'amortized_loan.pdf', 'paper_height':20.0, 'paper_width':20.0, 'block_params':[block_1_params,block_2_params], 'transformations':[('rotate',0.01),('scale paper',)], 'title_str':r'Amortized loan calculator \copyright Leif Roschier 2008', 'title_x': 17, 'title_y': 21, 'title_box_width': 5 } Nomographer(main_params)
