(maxima.info)Functions and Variables for finance
59.2 Functions and Variables for finance
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-- Function: days360 (<year1>,<month1>,<day1>,<year2>,<month2>,<day2>)
Calculates the distance between 2 dates, assuming 360 days years,
30 days months.
Example:
(%i1) load("finance")$
(%i2) days360(2008,12,16,2007,3,25);
(%o2) - 621
-- Function: fv (<rate>,<PV>,<num>)
We can calculate the future value of a Present one given a certain
interest rate. <rate> is the interest rate, <PV> is the present
value and <num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) fv(0.12,1000,3);
(%o2) 1404.928
-- Function: pv (<rate>,<FV>,<num>)
We can calculate the present value of a Future one given a certain
interest rate. <rate> is the interest rate, <FV> is the future
value and <num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) pv(0.12,1000,3);
(%o2) 711.7802478134108
-- Function: graph_flow (<val>)
Plots the money flow in a time line, the positive values are in
blue and upside; the negative ones are in red and downside. The
direction of the flow is given by the sign of the value. <val> is
a list of flow values.
Example:
(%i1) load("finance")$
(%i2) graph_flow([-5000,-3000,800,1300,1500,2000])$
-- Function: annuity_pv (<rate>,<PV>,<num>)
We can calculate the annuity knowing the present value (like an
amount), it is a constant and periodic payment. <rate> is the
interest rate, <PV> is the present value and <num> is the number of
periods.
Example:
(%i1) load("finance")$
(%i2) annuity_pv(0.12,5000,10);
(%o2) 884.9208207992202
-- Function: annuity_fv (<rate>,<FV>,<num>)
We can calculate the annuity knowing the desired value (future
value), it is a constant and periodic payment. <rate> is the
interest rate, <FV> is the future value and <num> is the number of
periods.
Example:
(%i1) load("finance")$
(%i2) annuity_fv(0.12,65000,10);
(%o2) 3703.970670389863
-- Function: geo_annuity_pv (<rate>,<growing_rate>,<PV>,<num>)
We can calculate the annuity knowing the present value (like an
amount), in a growing periodic payment. <rate> is the interest
rate, <growing_rate> is the growing rate, <PV> is the present value
and <num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) geo_annuity_pv(0.14,0.05,5000,10);
(%o2) 802.6888176505123
-- Function: geo_annuity_fv (<rate>,<growing_rate>,<FV>,<num>)
We can calculate the annuity knowing the desired value (future
value), in a growing periodic payment. <rate> is the interest
rate, <growing_rate> is the growing rate, <FV> is the future value
and <num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) geo_annuity_fv(0.14,0.05,5000,10);
(%o2) 216.5203395312695
-- Function: amortization (<rate>,<amount>,<num>)
Amortization table determined by a specific rate. <rate> is the
interest rate, <amount> is the amount value, and <num> is the
number of periods.
Example:
(%i1) load("finance")$
(%i2) amortization(0.05,56000,12)$
"n" "Balance" "Interest" "Amortization" "Payment"
0.000 56000.000 0.000 0.000 0.000
1.000 52481.777 2800.000 3518.223 6318.223
2.000 48787.643 2624.089 3694.134 6318.223
3.000 44908.802 2439.382 3878.841 6318.223
4.000 40836.019 2245.440 4072.783 6318.223
5.000 36559.597 2041.801 4276.422 6318.223
6.000 32069.354 1827.980 4490.243 6318.223
7.000 27354.599 1603.468 4714.755 6318.223
8.000 22404.106 1367.730 4950.493 6318.223
9.000 17206.088 1120.205 5198.018 6318.223
10.000 11748.170 860.304 5457.919 6318.223
11.000 6017.355 587.408 5730.814 6318.223
12.000 0.000 300.868 6017.355 6318.223
-- Function: arit_amortization (<rate>,<increment>,<amount>,<num>)
The amortization table determined by a specific rate and with
growing payment can be claculated by 'arit_amortization'. Notice
that the payment is not constant, it presents an arithmetic
growing, increment is then the difference between two consecutive
rows in the "Payment" column. <rate> is the interest rate,
<increment> is the increment, <amount> is the amount value, and
<num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) arit_amortization(0.05,1000,56000,12)$
"n" "Balance" "Interest" "Amortization" "Payment"
0.000 56000.000 0.000 0.000 0.000
1.000 57403.679 2800.000 -1403.679 1396.321
2.000 57877.541 2870.184 -473.863 2396.321
3.000 57375.097 2893.877 502.444 3396.321
4.000 55847.530 2868.755 1527.567 4396.321
5.000 53243.586 2792.377 2603.945 5396.321
6.000 49509.443 2662.179 3734.142 6396.321
7.000 44588.594 2475.472 4920.849 7396.321
8.000 38421.703 2229.430 6166.892 8396.321
9.000 30946.466 1921.085 7475.236 9396.321
10.000 22097.468 1547.323 8848.998 10396.321
11.000 11806.020 1104.873 10291.448 11396.321
12.000 -0.000 590.301 11806.020 12396.321
-- Function: geo_amortization (<rate>,<growing_rate>,<amount>,<num>)
The amortization table determined by rate, amount, and number of
periods can be found by 'geo_amortization'. Notice that the
payment is not constant, it presents a geometric growing,
<growing_rate> is then the quotient between two consecutive rows in
the "Payment" column. <rate> is the interest rate, <amount> is the
amount value, and <num> is the number of periods.
Example:
(%i1) load("finance")$
(%i2) geo_amortization(0.05,0.03,56000,12)$
"n" "Balance" "Interest" "Amortization" "Payment"
0.000 56000.000 0.000 0.000 0.000
1.000 53365.296 2800.000 2634.704 5434.704
2.000 50435.816 2668.265 2929.480 5597.745
3.000 47191.930 2521.791 3243.886 5765.677
4.000 43612.879 2359.596 3579.051 5938.648
5.000 39676.716 2180.644 3936.163 6116.807
6.000 35360.240 1983.836 4316.475 6300.311
7.000 30638.932 1768.012 4721.309 6489.321
8.000 25486.878 1531.947 5152.054 6684.000
9.000 19876.702 1274.344 5610.176 6884.520
10.000 13779.481 993.835 6097.221 7091.056
11.000 7164.668 688.974 6614.813 7303.787
12.000 0.000 358.233 7164.668 7522.901
-- Function: saving (<rate>,<amount>,<num>)
The table that represents the values in a constant and periodic
saving can be found by 'saving'. <amount> represents the desired
quantity and num the number of periods to save.
Example:
(%i1) load("finance")$
(%i2) saving(0.15,12000,15)$
"n" "Balance" "Interest" "Payment"
0.000 0.000 0.000 0.000
1.000 252.205 0.000 252.205
2.000 542.240 37.831 252.205
3.000 875.781 81.336 252.205
4.000 1259.352 131.367 252.205
5.000 1700.460 188.903 252.205
6.000 2207.733 255.069 252.205
7.000 2791.098 331.160 252.205
8.000 3461.967 418.665 252.205
9.000 4233.467 519.295 252.205
10.000 5120.692 635.020 252.205
11.000 6141.000 768.104 252.205
12.000 7314.355 921.150 252.205
13.000 8663.713 1097.153 252.205
14.000 10215.474 1299.557 252.205
15.000 12000.000 1532.321 252.205
-- Function: npv (<rate>,<val>)
Calculates the present value of a value series to evaluate the
viability in a project. <val> is a list of varying cash flows.
Example:
(%i1) load("finance")$
(%i2) npv(0.25,[100,500,323,124,300]);
(%o2) 714.4703999999999
-- Function: irr (<val>,<IO>)
IRR (Internal Rate of Return) is the value of rate which makes Net
Present Value zero. <flowValues> is a list of varying cash flows,
<I0> is the initial investment.
Example:
(%i1) load("finance")$
(%i2) res:irr([-5000,0,800,1300,1500,2000],0)$
(%i3) rhs(res[1][1]);
(%o3) .03009250374237132
-- Function: benefit_cost (<rate>,<input>,<output>)
Calculates the ratio Benefit/Cost. Benefit is the Net Present
Value (NPV) of the inputs, and Cost is the Net Present Value (NPV)
of the outputs. Notice that if there is not an input or output
value in a specific period, the input/output would be a zero for
that period. <rate> is the interest rate, <input> is a list of
input values, and <output> is a list of output values.
Example:
(%i1) load("finance")$
(%i2) benefit_cost(0.24,[0,300,500,150],[100,320,0,180]);
(%o2) 1.427249324905784
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