ComputeSoup: Web Computational Engine

Q (v8.5 – June 17, 2010)

© 2005-2010 Mark Furtney. All rights reserved.

ComputeSoup – Web Computational Engine

(Equation/Expression Evaluation)

Expr
Enter expression in this box

ComputeSoup: 81 Special Functions
(must be only term in expression)

Numbers, constants, variables, and most of the functions may be used anywhere in an expression, but some functions must be the only term in the expression. These functions are special because they do not return a single value, but rather they return a table of data or textual information, and thus cannot participate in building a more complex expression.

ComputeSoup – 81 Special Functions

AltBase	Cubic	Holiday	PayoffBiweekly	RacePace
Base	DayOfWeek	Integrate	PayoffBiweekly2	RaceTime
BillSplit	DayOfYear	IraProfile	PayoffExtra	Ratios
Binary	DayOfYear2	Karvonen	PayoffExtra2	Refinance
Calories	DaysAway	Line	PayoffLump	RegPolygon
Capacitance	DaysBetw	Line3D	PayoffProfile	RegPolygon2
Cartesian	DaysSince	MidPt	PayoffProfile2	Resistance
Colors	DaysTil	MidPt3D	PayoffSurvey	Rgb
ComplexAdd	EasterDate	NominalRate	PayoffView	RgbCompare
ComplexDiv	EffectiveRate	Normalize	PayoffView2	Solver
ComplexExp	Factor	Normalize2	Points	Stats
ComplexLn	Fitness	Normalize3	Polar	Tip
ComplexMult	HeartRate	Octal	PricePer	Unknowns
ComplexPower	HeatIndex	OhmsLaw	Quadratic	WindChill
ComplexPower2	HeatIndexMetric	Payoff	Quadrature	WindChillMetric
ComplexRoots	Hex	Payoff2	Quartic	Ymxb
ComplexSqrt

ComputeSoup – 81 Special Functions

Prototypes (full descriptions below)

Expr Use?	Prototype [ → ResultType ]	Expr Use?	Prototype [ → ResultType ]
No	AltBase( int, newBase )	No	NominalRate( effectiveRate, nPerYear ) → text
No	Base( int )	No	Normalize( x1, x2, ... ) → mult
No	BillSplit( bill, nShares, tipPercent ) → text	No	Normalize2( x1, x2, ... ) → mult
No	Binary( int )	No	Normalize3( x1, x2, ... ) → mult
No	Calories( activity, weight, dist, min, sec ) → text	No	Octal( int )
No	Capacitance( c1, c2, ... ) → text	No	OhmsLaw( power, voltage, current, resistance ) → text
No	Cartesian( dist, angle ) → Pair	No	Payoff( principal, rate, years, extra ) → table
No	Colors( value1, value2, ... ) → table	No	Payoff2( payment, rate, balance, extra ) → table
No	ComplexAdd( real1, imag1, real2, imag2 ) → (r, i)	No	PayoffBiweekly( principal, rate, years, extra ) → table
No	ComplexDiv( real1, imag1, real2, imag2 ) → (r, i)	No	PayoffBiweekly2( payment, rate, balance, extra ) → table
No	ComplexExp( real, imag ) → (r, i)	No	PayoffExtra( principal, rate, years, extra ) → table
No	ComplexLn( real, imag ) → (r, i)	No	PayoffExtra2( payment, rate, balance, extra ) → table
No	ComplexMult( real1, imag1, real2, imag2 ) → (r, i)	No	PayoffLump( payment, rate, balance, lumpSum ) → table
No	ComplexPower( real, imag, x ) → (r, i)	No	PayoffProfile( principal, rate, years, extra, nYears ) → text
No	ComplexPower2( real1, imag1, real2, imag2 ) → (r, i)	No	PayoffProfile2( payment, rate, balance, extra, nYears ) → text
No	ComplexRoots( nRoots, real, imag ) → (r,i)s	No	PayoffSurvey( payment, rate, balance ) → table
No	ComplexSqrt( real, imag ) → (r, i)	No	PayoffView( principal, rate, years ) → text
No	Cubic( a, b, c, d ) → 3 (r, i)s	No	PayoffView2( payment, rate, balance ) → text
No	DayOfWeek( year, month, day ) → text	No	Points( activity, weight, dist, min, sec ) → text
No	DayOfYear( year, month, day ) → text	No	Polar( x, y ) → Pair
No	DayOfYear2( year, dayNumb ) → text	No	PricePer( p1,n1, p2,n2, ... ) → table
No	DaysAway( nDays, year, month, day ) → text	No	Quadratic( a, b, c ) → 2 (r, i)s
Expr Use?	Prototype [ → ResultType ]	Expr Use?	Prototype [ → ResultType ]
No	DaysBetw( year1, month1, day1, year2, month2, day2 ) → text	No	Quadrature( a, b, expr ) → text
No	DaysSince( holiday ) → text	No	Quartic( a, b, c, d, e ) → 4 (r, i)s
No	DaysTil( holiday ) → text	No	RacePace( distance, hours, minutes, seconds ) → text
No	EasterDate( year ) → text	No	RaceTime( distance, minutes, seconds ) → text
No	EffectiveRate( nominalRate, nPerYear ) → text	No	Ratios( v1,n1, v2,n2, ... ) → table
No	Factor( int ) → mult	No	Refinance( currBalance, currPayment, currRate, newRate, loanCharge, loanLoan, newDuration ) → table
No	Fitness( code, gender, age, val1, val2 ) → text	No	RegPolygon( nSides, length ) → table
No	HeartRate( age, restingPulse ) → text	No	RegPolygon2( nSides, radius ) → table
No	HeatIndex( temp, humidity ) → text	No	Resistance( r1, r2, ... ) → text
No	HeatIndexMetric( temp, humidity ) → text	No	Rgb( value, flag ) → table
No	Hex( int )	No	RgbCompare( value1, value2, ... ) → table
No	Holiday( month ) → table	No	Solver( nEqns, x1, x2, ... ) → mult
No	Integrate( a, b, expr ) → text	No	Stats( x1, x2, x3, ... ) → mult
No	IraProfile( currValue, addition, rate, years ) → table	No	Tip( bill ) → table
No	Karvonen( age, restingPulse ) → text	No	Unknowns( nEqns, x1, x2, ... ) → mult
No	Line( x1, y1, x2, y2 ) → text	No	WindChill( temp, windSpeed ) → text
No	Line3D( x1, y1, z1, x2, y2, z2 ) → text	No	WindChillMetric( temp, windSpeed ) → text
No	MidPt( x1, y1, x2, y2 ) → text	No	Ymxb( x1, y1, x2, y2 ) → text
No	MidPt3D( x1, y1, z1, x2, y2, z2 ) → text
Expr Use?	Prototype [ → ResultType ]	Expr Use?	Prototype [ → ResultType ]

ComputeSoup – 81 Special Functions

Function Args Results Prototype/Description Expr Use?

AltBase 2 1 AltBase( int, newBase ): Display int in base newBase. Both arguments are integers, and (2 ≤ newBase ≤ 36) No

Base 1 3 Base( int ): Display the integer argument int in octal, hex and binary No

BillSplit 3 text BillSplit( bill, nShares, tipPercent ): The (rounded) amount each of nShares people should pay towards a total bill of (bill + tip), where tip is tipPercent of bill. Note that (nShares > 1) and need not be an integer, and (0 ≤ tipPercent &le 100). See also Tip(). No

Binary 1 1 Binary( int ): Display the integer argument int in binary No

Calories

text

Calories( activity, weight, dist, min, sec ): Approximate calories consumed by various activities. Arguments as in the table below. For example: "Calories( running, 165, 3.25, 25, 20 )" yields "408 calories -- Running (165 lbs, 3.25mi in 25:20 => 7:48/mi = 7.70 mph)". See also Fitness(), HeartRate(), Karvonen(), Points(), Bmi()

activity	weight	dist	min	sec	\|	‡ Others
Walking	lbs	miles	min	sec	\|	Aerobicdance, Aerobicshi†, Aerobicslo†, Basketball,
Running	lbs	miles	min	sec	\|	Handball, Hockey, Iceskating, Judo, Karate, Lacrosse,
Cycling	lbs	miles	min	sec	\|	Pingpong, Racketball, Rollerblading, Rollerskating,
Swimmingmy†	lbs	yards	min	sec	\|	Rowing, Skiingcc†, Skiingdh†, Skiingwater,
Swimmingfy†	lbs	yards	min	sec	\|	Snowshoeing, Snowshoveling, Soccer, Squash,
Swimmingmm†	lbs	meters	min	sec	\|	Taichi, Tennisd†, Tenniss†, Volleyball,
Swimmingfm†	lbs	meters	min	sec	\|	Wateraerobics
Skiprope	lbs	rpm	min	sec	\|	† Swimming__; my=(male,yards), fy=(female,yards);
Golfcarry	lbs	# holes	min	sec	\|	mm=(male,meters), fm=(female,meters);
Golfwalk	lbs	# holes	min	sec	\|	† Aerobics__; lo=low-impact, hi=high-impact
Others ‡	lbs	0	min	sec	\|	† Skiing__; cc=cross-country, dh=downhill
Stepcount	lbs	# steps	0	0	\|	† Tennis_; d=doubles, s=singles

Capacitance 2-10 text Capacitance( c1, c2, ... ): Capacitance for 2-10 capacitors (c1, c2, ...) in serial, parallel. All args > 0. No

Cartesian 2 Pair Cartesian( dist, angle ): The (x,y) coordinates of the point defined as dist units from the origin at the angle angle radians (that is, the arguments are the polar coordinates of the point) No

Colors 1,2,.. table Colors( value1, value2, ... ): Display the color and the Red, Green and Blue components of the values (max=16) in a table. Value is an integer representation of the color (e.g., 0x3DB733), and is silently kept in the range (0 - 0xFFFFFF). The values are sorted and duplicate values are silently ignored. See also Rgb(). Same as RgbCompare(). No

ComplexAdd 4 (r, i) ComplexAdd( real1, imag1, real2, imag2 ): Addition of two complex numbers:
ComplexAdd(a,b,c,d) = (a+bi) + (c+di) = ((a+c) + (b+d)i) No

ComplexDiv 4 (r, i) ComplexDiv( real1, imag1, real2, imag2 ): Division of complex numbers:
ComplexDiv(a,b,c,d) = (a+bi)/(c+di) No

ComplexExp 2 (r, i) ComplexExp( real, imag ): Exponential of a complex number.
ComplexExp(a,b) = e^(a+bi) No

ComplexLn 2 (r, i) ComplexLn( real, imag ): Natural logarithm of a complex number. No

ComplexMult 4 (r, i) ComplexMult( real1, imag1, real2, imag2 ): Product of two complex numbers:
ComplexMult(a,b,c,d) = (a+bi)*(c+di) No

Function Args Results Prototype/Description Expr Use?

ComplexPower 3 (r, i) ComplexPower( real, imag, x ): Raise a complex number to a real power.
ComplexPower(a,b,c) = (a+bi)^c No

ComplexPower2 4 (r, i) ComplexPower2( real1, imag1, real2, imag2 ): Raise a complex number to a complex power.
ComplexPower2(a,b,c,d) = (a+bi)^(c+di) No

ComplexRoots 3 (r,i)s ComplexRoots( nRoots, real, imag ): The nRoots roots of a complex number. For nRoots = 3, the 3 cuberoots are generated No

ComplexSqrt 2 (r, i) ComplexSqrt( real, imag ): The positive square root of a complex number. When the result is (x + yi), the other root is (–x – yi). Note that x ≥ 0 (always) No

Cubic 4 3 (r, i)s Cubic( a, b, c, d ): The roots to the 3^rd order equation:
ax³ + bx² + cx + d = 0, where (a ≠ 0) No

DayOfWeek 3 text DayOfWeek( year, month, day ): Print day-of-week for input date: year > 1752, month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay), (28 ≤ lastDay=f(month,year) ≤ 31). If the input is (0,0,0), use today. See also DayOfYear(), DayOfYear2(). No

DayOfYear 3 text DayOfYear( year, month, day ): Print day-of-year for input date: year > 1752, month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay), (28 ≤ lastDay=f(month,year) ≤ 31). If the input is (0,0,0), use today. See also DayOfWeek(), DayOfYear2(). No

DayOfYear2 2 text DayOfYear2( year, dayNumb ): Print the date (day-of-week, month, day) for the dayNumb^th day of year year, (1753 ≤ year ≤ 9999), (1 ≤ dayNumb ≤ 366). See also DayofYear(), DayOfWeek(). No

DaysAway 4 text DaysAway( nDays, year, month, day ): Display the date of the day which is nDays from year, month, day. (1752 < year < 10000), month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay) (28 ≤ lastDay=f(month,year) ≤ 31). If date is (0,0,0), use today. nDays may be positive or negative. Note that the computation of years/days goes in the direction of nDays. That is, DaysAway( 740, 1994,FEB,22 ) will yield: Tuesday, February 22, 1994 → Sunday, March 3, 1996 = 740 days = 2 years, 10 days, but DaysAway( -740, 1996, MAR, 3 ) will yield: Tuesday, February 22, 1994 ← Sunday, March 3, 1996 = 740 days = 2 years, 9 days. See also DaysBetw(). No

DaysBetw 6 text DaysBetw( year1, month1, day1, year2, month2, day2 ): Display the number of days between date1 (1^st 3 arguments) and date2 (2^nd 3 arguments). (1752 < year < 10000), month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay) (28 ≤ lastDay=f(month,year) ≤ 31). If date* is (0,0,0), use today. Note that the computation of years/days goes from the first date to the second date. That is, DaysBetw( 2007, FEB, 15, 2008, MAR, 25 ) will yield: Thursday, February 15, 2007 → Tuesday, March 25, 2008 = 404 days = 1 year, 39 days, but DaysBetw( 2008, MAR, 25, 2007, FEB, 15 ) will yield: Thursday, February 15, 2007 ← Tuesday, March 25, 2008 = 404 days = 1 year, 38 days. See also DaysAway(). No

DaysSince 1, 2 text DaysSince( holiday ) -or- DaysSince( month, day ): Display number of days since the last occurrence of the specified date. Holiday may be one of { CHRISTMAS, THANKSGIVING, VALENTINES, MOTHERS, FATHERS, SUMMER, FALL, WINTER, SPRING, LABOR, MEMORIAL, JAN, FEB, ... DEC }, among others. Month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay) (28 ≤ lastDay=f(month,year) ≤ 31). Click Constants for a full list. See also DaysTil(), DaysAway(), DaysBetw(). No

DaysTil 1, 2 text DaysTil( holiday ) -or- DaysTil( month, day ): Display number of days til the next occurrence of the specified date. Holiday may be one of { CHRISTMAS, THANKSGIVING, VALENTINES, MOTHERS, FATHERS, SUMMER, FALL, WINTER, SPRING, LABOR, MEMORIAL, JAN, FEB, ... DEC }, among others. Month (1-12) for (Jan-Dec) or the constants JAN, FEB, ... DEC, and day (1-lastDay) (28 ≤ lastDay=f(month,year) ≤ 31). Click Constants for a full list. See also DaysSince(), DaysAway(), DaysBetw(). No

Function Args Results Prototype/Description Expr Use?

EasterDate 1 text EasterDate( year ): Easter for year = year > 1752 (Easter falls between March 22 and April 25) No

EffectiveRate 2 text EffectiveRate( nominalRate, nPerYear ): The effective annual rate for a nominal interest rate nominalRate, compounded nPerYear times per year. NominalRate must be > 0, and nPerYear is an integer > 1. The "nominal rate" is the rate per compound period. For example, if a credit card charges a nominal 1.5%/month, the effective annual rate is 19.5618% (not 18%). See also NominalRate(). No

Factor 1 mult Factor( int ): List all the prime values which divide evenly (with no remainder) into integer int. Max value for int is (2³¹-1) = 2,147,483,647 No

Fitness

text

Fitness( code, gender, age, val1, val2 ): Determine fitness level by taking one of six basic fitness tests (based on Dr Kenneth Cooper's "Aerobics" books). The tests are either Distance traveled in a specified time or Time to cover a specified distance for walking, running, swimming or cycling. Result is one of {VeryPoor, Poor, Fair, Good, Excellent, Superior}. Consult a physician before taking any of these tests. Warm up appropriately before starting a test. See also HeartRate(), Karvonen(), Points(), Calories(), Bmi(). code = test code (1-6), gender is gender (0,1) = (Male,Female), age is age (years), val1 and val2 are as below

Test	code	gender	age	val1	val2	\|	Test	code	gender	age	val1	val2
1.5 mi run	1	(0,1)	yrs	min	sec	\|	12 min cycling	4	(0,1)	yrs	mi	0
3.0 mi walk	2	(0,1)	yrs	min	sec	\|	12 min swimming	5	(0,1)	yrs	yds	0
12 min walk/run	3	(0,1)	yrs	mi	0	\|	12 min swimming	6	(0,1)	yrs	m	0

HeartRate 2 text HeartRate( age, restingPulse ): Display maximum and various other workout-related target heart rates: age is age (integer, (10-100)), and restingPulse is resting heart rate (integer, (35-90)). Same as Karvonen(). No

HeatIndex 2 text HeatIndex( temp, humidity ): Display the heat index for a given temperature temp (°F) and relative humidity humidity (%). The heat index is an approximation of the temperature humans perceive. (temp > 68°F, humidity > 40). No

HeatIndexMetric 2 text HeatIndexMetric( temp, humidity ): Display the heat index for a given temperature temp (°C) and relative humidity humidity (%). The heat index is an approximation of the temperature humans perceive. (temp > 20°C, humidity > 40). No

Hex 1 1 Hex( int ): Display the integer argument int in hexadecimal No

Holiday 1 table Holiday( month ): List the holidays in month month. If month is not in JAN – DEC (1–12), list all the holidays. No

Integrate 3 text Integrate( a, b, expr ): _{_a}∫^{^b}{expr(x)} dx. Approximate result of integrating the expression (expr) from a to b. A and b are the lower and upper bounds of the (dummy) variable in expr, and must be constants with (a ≠ b). The expression expr must have exactly one variable, must be single-valued, and may be a single user-defined function or an expression with no user-defined functions. The expression expr must be continuous over the specified range, and may include any single-valued function except Rand() and IRand(). Unpredictable results may occur when expr is not continuous or is otherwise ill-behaved. Same as Quadrature(), except Quadrature() always shows convergence of the approximate solution. Quadrature() is recommended. No

IraProfile 4 table IraProfile( currValue, addition, rate, years ): Show lifetime investment progress (e.g., an IRA). currValue is the current value, addition is the yearly addition to (or withdrawal from) ithe investment, rate is the annual interest rate (e.g., 5.25), and years is the lifetime (years). IraProfile() assumes Jan 1 investments and reports results for each Dec 31. See also Ira(), FutureValue() No

Karvonen 2 text Karvonen( age, restingPulse ): Display maximum and various other workout-related target heart rates: age is age (integer, (10-100)), and restingPulse is resting heart rate (integer, (35-90)). Same as HeartRate(). No

Function Args Results Prototype/Description Expr Use?

Line 4 text Line( x1, y1, x2, y2 ): Given two data points on the X-Y plane, (x1, y1) and (x2, y2), compute the slope (m), the y-intercept (b), the distance between the two points, the midpoint, and show the equation of the line containing the points. Same as Ymxb(). See also Line3D(). No

Line3D 6 text Line3d( x1, y1, z1, x2, y2, z2 ): Given two data points in 3D space (X-Y-Z), (x1, y1, z1) and (x2, y2, z2), compute the the equation of the line, the distance between the 2 points, the direction vector from point1 to point2, the midpoint, and the X-Y, X-Z, Y-Z slopes. See also Line(). No

MidPt 4 text MidPt( x1, y1, x2, y2 ): Given two data points on the X-Y plane, (x1, y1) and (x2, y2), display the coordinates of the midpoint of the line defined by the two points. See also Line(), Ymxb(), MidPt3D(). No

MidPt3D 6 text MidPt3D( x1, y1, z1, x2, y2, z2 ): Given two data points in 3-D space, (x1, y1, z1) and (x2, y2, z2), display the coordinates of the midpoint of the line defined by the two points. See also MidPt(), Line3D() No

NominalRate 2 text NominalRate( effectiveRate, nPerYear ): The nominal rate for an effective annual interest rate (effectiveRate), compounded nPerYear times per year. (effectiveRate > 0), and nPerYear is an integer > 1. The "nominal rate" is the rate per compound period. See also EffectiveRate(). No

Normalize 2,3,.. mult Normalize( x1, x2, ... ): Normalize a multi-element vector. At least one element must be non-zero. Divide each element by the vector length := Sqrt(sum of the squares of the elements) No

Normalize2 2,3,.. mult Normalize2( x1, x2, ... ): Normalize a multi-element vector. At least one element must be non-zero. Divide each element by the value of the largest of the absolute values of the elements. Normalize() is the more mathematically rigorous form. No

Normalize3 2,3,.. mult Normalize3( x1, x2, ... ): Normalize a multi-element vector. At least one element must be non-zero. Divide each element by the sum of the absolute values of the elements. Normalize() is the more mathematically rigorous form. No

Octal 1 1 Octal( int ): Display the integer argument int in octal. No

OhmsLaw 4 text OhmsLaw( power, voltage, current, resistance ): Compute electrical parameters. Set two of the four arguments to zero and two to non-zero to compute the value of the two zero arguments:
power = Power (watts)
voltage = Voltage (volts)
current = Current (amps)
resistance = Resistance (ohms) No

Payoff 4 table Payoff( principal, rate, years, extra ): Show impact of extra amount submitted with each mortgage payment starting at the first payment:
principal = Initial loan amount (principal)
rate = Annual interest rate (percent - e.g., 7.25)
years = Number of years of initial loan
extra = Extra amount with each payment (must be > 0)
Same as PayoffExtra(). See also Refinance(), Mortgage(), and the other Payoff*() functions. No

Payoff2 4 table Payoff2( payment, rate, balance, extra ): Show impact of extra amount submitted with each future mortgage payment when the loan is partly paid off:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 7.125)
balance = Current balance (principal)
extra = Extra amount with each payment (must be > 0)
Same as PayoffExtra2(). See also Refinance(), Mortgage(), and the other Payoff*() functions. No

Function Args Results Prototype/Description Expr Use?

PayoffBiweekly 4 table PayoffBiweekly ( principal, rate, years, extra ): Show impact of bi-weekly mortgage payments starting at the first payment. This technique calls for making payments every other week, each at exactly ½ of the monthly payment. Paying more per year (approximately 13/12 as much) leads to a reduced total out-of-pocket expenditure. Note that the real advantage of this technique is convenience (payments synchronized with bi-weekly paychecks) – one could realize about the same out-of-pocket savings by paying 1/12^th more with each regular monthly payment. This computation assumes that there is no extra charge for this payment schedule. When the 4^th argument (extra) is non-zero, show the impact of adding this amount to each biweekly payment.
principal = Initial loan amount (principal)
rate = Annual interest rate (percent - e.g., 5.875)
years = Number of years of initial loan
extra = Extra amount with each biweekly payment (must be ≥ 0)
(Set extra to zero to get biweekly impact only)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffBiweekly2 4 table PayoffBiweekly2 ( payment, rate, balance, extra ): Show impact of shifting to bi-weekly mortgage payments for a partly paid off loan. This technique calls for making payments every other week, each at exactly ½ of the previous monthly payment. Paying more per year (approximately 13/12 as much) leads to a reduced total out-of-pocket expenditure. Note that the real advantage of this technique is convenience (payments synchronized with bi-weekly paychecks) – one can realize about the same out-of-pocket savings by paying 1/12^th more with each regular monthly payment. This computation assumes that there is no extra charge for this payment schedule. When the 4^th argument (extra) is non-zero, show the impact of adding this amount to each biweekly payment.
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 6.35)
balance = Current balance (principal)
extra = Extra amount with each biweekly payment (must be ≥ 0)
(Set extra to zero to get biweekly impact only)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffExtra 4 table PayoffExtra( principal, rate, years, extra ): Show impact of extra amount submitted with each mortgage payment starting at the first payment:
principal = Initial loan amount (principal)
rate = Annual interest rate (percent - e.g., 7.25)
years = Number of years of initial loan
extra = Extra amount with each payment (must be > 0)
Same as Payoff(). See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffExtra2 4 table PayoffExtra2( payment, rate, balance, extra ): Show impact of extra amount submitted with each future mortgage payment when the loan is partly paid off:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 7.125)
balance = Current balance (principal)
extra = Extra amount with each payment (must be > 0)
Same as Payoff2(). See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffLump 4 table PayoffLump( payment, rate, balance, lumpSum ): Show impact of a single lump sum payment on a partly paid off mortgage payoff profile:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 6.625)
balance = Current balance (principal)
lumpSum = Lump sum payment (must be > 0)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffProfile 5 text PayoffProfile( principal, rate, years, extra, nYears ): Show a payoff profile (with monthly details) while paying off a new mortgage starting at the first payment. Set extra to zero to get the standard payoff profile:
principal = Initial loan amount (principal)
rate = Annual interest rate (percent - e.g., 5.875)
years = Number of years of initial loan
extra = Extra amount with each payment (must be ≥ 0)
nYears = Number of years for which to show monthly results (1-5, silently enforced)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffProfile2 5 text PayoffProfile2( payment, rate, balance, extra, nYears ): Show a payoff profile (with monthly details) while paying off a partly paid off mortgage. Set extra to zero to get the standard payoff profile:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 5.75)
balance = Current balance (principal)
extra = Extra amount with each payment (must be ≥ 0)
nYears = Number of years for which to show monthly results (1-5, silently enforced)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffSurvey 3 table PayoffSurvey( payment, rate, balance ): Show impact of various (internally generated) prepayment options on a partly paid off mortgage payoff profile:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 6.5)
balance = Current balance (principal)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffView 3 text PayoffView( principal, rate, years ): Show characteristics of paying off a new mortgage at the normal rate starting at the first payment
principal = Initial loan amount (principal)
rate = Annual interest rate (percent - e.g., 5.875)
years = Number of years of initial loan
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

PayoffView2 3 text PayoffView2( payment, rate, balance ): Show characteristics of paying off a partly paid off mortgage at the normal rate:
payment = Monthly payment (principal + interest only: no escrow)
rate = Annual interest rate (percent - e.g., 5.75)
balance = Current balance (principal)
See also Refinance(), Mortgage(), and the other Payoff*() functions. No

Points

text

Points( activity, weight, dist, min, sec ): Aerobic Points for various activities - based on Dr Kenneth Cooper's bestseller, "Aerobics." General objective is to get a minimum of 4 workouts and 30 points per week of aerobic exercise to gain the training effect. Approximate calories consumed are also reported. Arguments as in the table below. For example: "Points(running, 142, FIVEK, 21, 27)" yields "20.1 pts -- Running: 142 lbs, 3.10686mi in 21:27 => 6:54/mi = 8.69 mph (335 cals)". See also Fitness(), HeartRate(), Karvonen(), Calories(), Bmi()

activity	weight	dist	min	sec	\|	‡ Others
Walking	lbs	miles	min	sec	\|	Aerobicdance, Aerobicshi†, Aerobicslo†, Basketball,
Running	lbs	miles	min	sec	\|	Handball, Hockey, Iceskating, Lacrosse, Racketball,
Cycling	lbs	miles	min	sec	\|	Rollerblading, Rollerskating, Rowing, Skiingcc†,
Swimmingmy†	lbs	yards	min	sec	\|	Skiingdh†, Skiingwater, Soccer, Squash, Tennisd†,
Swimmingfy†	lbs	yards	min	sec	\|	Tenniss†, Volleyball
Swimmingmm†	lbs	meters	min	sec	\|
Swimmingfm†	lbs	meters	min	sec	\|	† Swimming__; my=(male,yards), fy=(female,yards);
Skiprope	lbs	rpm	min	sec	\|	mm=(male,meters), fm=(female,meters);
Golfcarry	lbs	# holes	min	sec	\|	† Aerobics__; lo=low-impact, hi=high-impact
Golfwalk	lbs	# holes	min	sec	\|	† Skiing__; cc=cross-country, dh=downhill
Others ‡	lbs	0	min	sec	\|	† Tennis_; d=doubles, s=singles

Polar 2 Pair Polar( x, y ): The polar coordinates (distance from origin and angle (radians)) of the point defined by the cartesian coordinates (x, y) No

Function Args Results Prototype/Description Expr Use?

PricePer 2-12 table PricePer( p1,n1, p2,n2, ... ): Display the price per unit ratios p1/n1, p2/n2, ... (up to 6 pairs) for comparison purposes. n1, n2, ... ≠ 0. Similar to Ratios(). No

Quadratic 3 2 (r, i)s Quadratic( a, b, c ): The roots to the 2^nd order equation:
ax² + bx + c = 0, where (a ≠ 0) No

Quadrature 3 text Quadrature( a, b, expr ): _{_a}∫^{^b}{expr(x)} dx. Approximate result of integrating the expression (expr) from a to b. A and b are the lower and upper bounds of the (dummy) variable in expr, and must be constants with (a ≠ b). The expression expr must have exactly one variable, must be single-valued, and may be a single user-defined function or an expression with no user-defined functions. The expression expr must be continuous over the specified range, and may include any single-valued function except Rand() and IRand(). Unpredictable results may occur when expr is not continuous or is otherwise ill-behaved. Same as Integrate(), except Quadrature() always shows convergence of the approximate solution. Quadrature() is recommended. No

Quartic 5 4 (r, i)s Quartic( a, b, c, d, e ): The roots to the 4^th order equation:
ax⁴ + bx³ + cx²+ dx + e = 0, where (a ≠ 0) No

RacePace 4 text RacePace( distance, hours, minutes, seconds ): Pace (mm:ss/mi) for race of distance distance miles run in hours hours, minutes minutes, and seconds seconds. Note that distance may be a constant or an expression, e.g., MARATHON, TENK, FIVEK, 100/1760, 0.8*KM, METRICMILE, HALFMARATHON, etc No

RaceTime 3 text RaceTime( distance, minutes, seconds ): Time (hh:mm:ss) to run a race of distance distance miles run at a pace of minutes minutes and seconds seconds per mile. Note that distance may be a constant or an expression, e.g., MARATHON, TENK, FIVEK, METRICMILE, etc No

Ratios 2-12 table Ratios( v1,n1, v2,n2, ... ): Display the ratios v1/n1, v2/n2, ... (up to 6 pairs) for comparison purposes. n1, n2, ... ≠ 0. Similar to PricePer(). No

Refinance 7 table Refinance( currBalance, currPayment, currRate, newRate, loanCharge, loanLoan, newDuration ): Impact (total cost, breakeven, % interest, et cetera) of refinancing a loan:
currBalance - Current loan balance (principal)
currPayment - Current loan payment (principal and interest components only)
currRate - Current loan annual interest rate (percent - e.g., 7.125)
newRate - New loan annual interest rate (percent - e.g., 5.375)
loanCharge - Addition to principal (loan charge - e.g., closing costs, points)
loanLoan - Addition to principal ("equity" payout - may be 0)
newDuration - New loan duration (years)
Notes: (1) Do not include escrow payments (typically taxes and insurance) with currPayment, (2) See also Mortgage() and the Payoff*() functions No

RegPolygon 2 table RegPolygon( nSides, length ): Information about the nSides-sided regular polygon with side length. A regular polygon has all equal angles - which implies all equal sides (Note: all equal sides does not imply equal angles). (2 < nSides < 13), (length > 0). Name, angle, area, and the radii of the inscribed and circumscribed circles are given. See also RegPolygon2() No

RegPolygon2 2 table RegPolygon2( nSides, radius ): Information about the nSides-sided regular polygon with radius radius. (2 < nSides < 13), (radius > 0). Name, angle, area, and the radii of the inscribed and circumscribed circles are given. See also RegPolygon() No

Resistance 2-10 text Resistance( r1, r2, ... ): Resistance for 2-10 resistors (r1, r2, ...) in serial, parallel. All args > 0. No

Rgb 2 table Rgb( value, flag ): Display the Red, Green and Blue components of value in a table. When flag is not zero, display an iPhone/iPod-iTouch/iPad SDK Objective-C format representation. Value is an integer representation of the color (e.g., 0x66FF33), and is silently kept in the range (0 - 0xFFFFFF). See also RgbCompare(). No

RgbCompare 1,2,.. table RgbCompare( value1, value2, ... ): Display the color and the Red, Green and Blue components of the values (max=16) in a table. Value is an integer representation of the color (e.g., 0xB391A8), and is silently kept in the range (0 - 0xFFFFFF). The values are sorted and duplicate values are silently ignored. See also Rgb(). Same as Colors(). No

Solver many mult Solver( nEqns, x1, x2, ... ): Solve nEqns equations in nEqns unknowns (1 ≤ nEqns ≤ 8). There are (nEqns*(nEqns+1)) more arguments, representing the equations. Solver() is the same as Unknowns(). For example:
x + 2y + 3z = 4 2x + y + 4z = 5 3x + 3y + 6z = 12
For these equations, using Solver(3, 1,2,3,4, 2,1,4,5, 3,3,6,12)
yields: x = 7, y = 3, z = -3 No

Function Args Results Prototype/Description Expr Use?

Stats 3,4,.. mult Stats( x1, x2, x3, ... ): Report statistics about the arguments. Must have 3 or more arguments. Show: Number, Average, Standard Deviation, Median, Sum, Sum of the Squares, Max and MaxLoc, Min and MinLoc No

Tip 1 table Tip( bill ): Array of tip candidates for bill bill. See also BillSplit(). No

Unknowns many mult Unknowns( nEqns, x1, x2, ... ): Solve nEqns equations in nEqns unknowns (1 ≤ nEqns ≤ 8). There are (nEqns*(nEqns+1)) more arguments, representing the equations. Unknowns() is the same as Solver(). For example:
w + x + y + z = 10 w + 2x + y + 6z = 32 2w + y + z = 9 3w + 2x + 5y + 4z = 38
For these equations, using Unknowns(4, 1,1,1,1,10, 1,2,1,6,32, 2,0,1,1,9, 3,2,5,4,38)
yields: w = 1 y = 3 x = 2 z = 4 No

WindChill 2 text WindChill( temp, windSpeed ): Display the windchill factor (°F) for a given temperature temp (°F) and wind speed windSpeed (mph). (temp < 50°F, windSpeed > 3 mph). The Windchill factor is the apparent temperature on exposed skin due to the wind. No

WindChillMetric 2 text WindChillMetric( temp, windSpeed ): Display the windchill factor (°C) for a given temperature temp (°C) and wind speed windSpeed (km/h). (temp < 10°C, windSpeed > 5 km/h). The Windchill factor is the apparent temperature on exposed skin due to the wind. No

Ymxb 4 text Ymxb( x1, y1, x2, y2 ): Given two data points on the X-Y plane, (x1, y1) and (x1, y2), compute the slope (m), the y-intercept (b), the distance between the two points, the midpoint, and show the equation of the line containing the points. Same as Line(). See also Line3D(). No

Function Args Results Prototype/Description Expr Use?

ComputeSoup - 78 Special Constants

ComputeSoup – Overview

This web site allows users to evaluate expressions (including those which have variables – each with one or more values), and display the results in an easy-to-read table. Many standard mathematical constants and functions are available for use in the expressions, as well as a collection of special purpose functions for a variety of computational chores (for example, calculating race pace, refinance and mortgage payoff strategies, performing integrations, calculating the number of calories burned by various workouts). The button (above left) allows you to get more details about these and other capabilities, and the other buttons above (e.g., , , , ) lead to information which may be useful in building computations. The button presents more detail about how to use this site effectively, the button brings up this page, and the button provides a mechanism for sending comments, questions and/or requests to us.

There are several advanced features, including storing results for later use, building user-defined functions, input shortcuts, and integration. Click → for details.

The major capability is to evaluate expressions and equations (including those that have variables) and print the results out in a table for easy review. Below are five samples:

1)	A simple equation with a constant, two functions, and two variables
2)	Calculate race times and race paces
3)	Calculate calories consumed during a bike ride and other actvities
4)	Investigate mortgage payoff strategies (various extra payments each month)
5)	Calculate the implications of refinancing a mortgage

Sample 1) tr = (pi-2.375)(sqrt(x)cos(omega-x))

Calculate values for tr for three values of x and three values of omega. This is a two-step operation: first enter the equation into the [Expr] box (as in the sample below) and click .

Expr

and second, enter value(s) for the variables (as in the sample below) and click .

x	5 7 10
omega	5.18, 9.1, 17.104

This will yield the results shown below:

tr = (PI-2.375)(Sqrt(x)Cos(omega-x));

		tr	x	omega
		------	---	---------
Max	1)	1.6864589	5	5.18
	2)	-0.9853364	5	9.1
	3)	1.534163	5	17.104
	4)	-0.500223	7	5.18
	5)	-1.0239357	7	9.1
Min	6)	-1.5780752	7	17.104
Mdn	7)	0.2603652	10	5.18
	8)	1.5068937	10	9.1
	9)	1.6523817	10	17.104

This sample illustrates the use of variables (x and omega), uses an equation (an equation is a result variable (tr), followed by "=" and an expression). The nine result values of tr are automatically saved in the Store. If you use tr in a subsequent computation during this session, those nine values will automatically be loaded (although you can edit or override them). One constant (PI) and two functions – Sqrt() and Cos() – are also used. The maximum, minimum and median value of the results are flagged. Further, note that whitespace is ignored in the [Expr] box, but that whitespace is important for entering variable values. Values are separated by any combination of one or more blanks and commas.

Sample 2) Using Race Functions

How long will it take to run a marathon at a steady pace of 7:15 per mile?

The Racetime() function has three arguments (distance, minutes, and seconds). It shows the time to cover the distance at the input pace. Enter the information into the [Expr] box and click .

Expr

which yields

Racetime(MARATHON, 7, 15);

The Marathon: 26.21875 mi at 7:15/mi (8.28 mph) => 3:10:05

In this sample, marathon is a constant. The Racepace() function performs the reverse operation – it takes 4 arguments (distance, hours, minutes, seconds) and reports overall pace for a given distance and time. In this sample, the variable xmin is used to check out the paces for various overall times.

Expr

Enter value(s) for xmin and click .

xmin	0 10 20 30 40 50

which yields

	Dist (mi)	Time	Pace
The Marathon:	26.21875	3:00:00	6:52/mi	(8.74 mph)
The Marathon:	26.21875	3:10:00	7:15/mi	(8.28 mph)
The Marathon:	26.21875	3:20:00	7:38/mi	(7.87 mph)
The Marathon:	26.21875	3:30:00	8:01/mi	(7.49 mph)
The Marathon:	26.21875	3:40:00	8:23/mi	(7.15 mph)
The Marathon:	26.21875	3:50:00	8:46/mi	(6.84 mph)

Sample 3) Calories burned

How many calories do you burn in a 50 minute, 13½ mile bike ride if you weigh 165 pounds?

You can use the Calories() function. Enter calories() in the [Expr] box and click to see the arguments. This yields the following table, which shows that the Calories() function can be used with 40 different activities (for this sample, we choose cycling):

Function

Args

Results

Prototype/Description

Expr Use?

Calories

text

activity	weight	dist	min	sec	\|	‡ Others
Walking	lbs	miles	min	sec	\|	Aerobicdance, Aerobicshi†, Aerobicslo†, Basketball,
Running	lbs	miles	min	sec	\|	Handball, Hockey, Iceskating, Judo, Karate, Lacrosse,
Cycling	lbs	miles	min	sec	\|	Pingpong, Racketball, Rollerblading, Rollerskating,
Swimmingmy†	lbs	yards	min	sec	\|	Rowing, Skiingcc†, Skiingdh†, Skiingwater,
Swimmingfy†	lbs	yards	min	sec	\|	Snowshoeing, Snowshoveling, Soccer, Squash,
Swimmingmm†	lbs	meters	min	sec	\|	Taichi, Tennisd†, Tenniss†, Volleyball,
Swimmingfm†	lbs	meters	min	sec	\|	Wateraerobics
Skiprope	lbs	rpm	min	sec	\|	† Swimming__; my=(male,yards), fy=(female,yards);
Golfcarry	lbs	# holes	min	sec	\|	mm=(male,meters), fm=(female,meters);
Golfwalk	lbs	# holes	min	sec	\|	† Aerobics__; lo=low-impact, hi=high-impact
Others ‡	lbs	0	min	sec	\|	† Skiing__; cc=cross-country, dh=downhill
Stepcount	lbs	# steps	0	0	\|	† Tennis_; d=doubles, s=singles

Enter the argument values into the [Expr] box (as below) and click .

Expr

which yields

Calories( CYCLING, 165, 13.5, 50, 0 );

517 calories -- Cycling (165 lbs, 13.5mi in 50:00 => 3:42/mi = 16.20 mph)

In this sample, cycling is a constant. Check the Prototype/Description table above for other activities which are supported by Calories(), for example, running, swimming, tennis, walking, aerobics, ....

Here are two more Calories() samples (running and walking).

Expr

which yields

Calories( RUNNING, 175, 3, 22, 40 );

402 calories -- Running (175 lbs, 3mi in 22:40 => 7:33/mi = 7.94 mph)

Expr

which yields

Calories( RUNNING, 140, 3.8, 63, 0 );

254 calories -- Walking (140 lbs, 3.8mi in 1:03:00 => 16:35/mi = 3.62 mph)

Sample 4) Paying off a loan early

Consider a mortgage at 6.55%, with payment of $1,331.76 per month, and an outstanding balance of $204,236.70 – what will be the impact of paying an extra $200 each month (assuming no prepayment penalties)? What about other amounts?

You can use the Payoff2() function. Enter payoff2() in the [Expr] box and click to see the arguments. This yields

Function	Args	Results	Prototype/Description	Expr Use?
Payoff2	4	table	*Payoff2( payment, rate, balance, extra* ): Show impact of extra amount submitted with each future mortgage payment when the loan is partly paid off: payment = Monthly payment (principal + interest only: no escrow) rate = Annual interest rate (percent - e.g., 5.85) balance = Current balance (principal) extra** = Extra amount with each payment Same as PayoffExtra2(). See also Refinance(), Mortgage(), and the other Payoff*() functions.	No

Enter the information into the [Expr] box (as below) and click .

Expr

which yields

Balance = $204,237 at 6.55% with monthly payments of $1,331.76
Total responsibility = 334 payments (333 * $1,331.76 + $447.13)
= $443,923 ($239,687 = 54.0% is interest)

An extra $200/month saves $77,785 (17.5%), pays off loan 94 months early

	Standard	$200 extra
	---------------	--------------
Balance	$204,237	$204,237
Payment	$1,331.76	$1,531.76
Last payment	$447.13	$47.65
Months	334	240
Interest	$239,687	$161,902
% Interest	54.0%	44.2%
	---------------	--------------
Total	$443,923	$366,138
	---------------	--------------
Savings	—	$77,785

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

This shows a set of results for paying an extra $200.00 with each monthy payment. The impacts are an overall savings of $77,785 (17.5%) and a reduction of almost eight years of payments.

To investigate the impact of other extra amounts per month, use various values for the extra variable. Enter:

Expr

Note the variable add – picking a set of values for add allows us to do a simple parameter study. That is, we can easily see the results of various extra payment amounts. Now click , then enter the additional amount(s) to pay for each month (values for add) and click to see the impact

Enter value(s) for add

add	50, 100, 168.24, 200, 250, 300, 400, 500

which yields

Balance = $204,237 at 6.55% with monthly payments of $1,331.76
Total responsibility = 334 payments (333 * $1,331.76 + $447.13)
= $443,923 ($239,687 = 54.0% is interest)

Monthly	Monthly	/-------------- Saves ------------\			Final	Total		Total
Extra	Payment	$	%	Months	Payment	Interest		Payments
-----------	-------------	-----------------------------------------			------------	------------------------		--------------
0	$1,331.76	—			$447.13	$239,687	54.0%	$443,923
$50	$1,381.76	$26,619	6.0%	31	$12.80	$213,068	51.1%	$417,304
$100	$1,431.76	$47,323	10.7%	56	$3.15	$192,364	48.5%	$396,601
$168.24	$1,500	$69,318	15.6%	84	$1,105.15	$170,368	45.5%	$374,605
$200	$1,531.76	$77,785	17.5%	94	$47.65	$161,902	44.2%	$366,138
$250	$1,581.76	$89,408	20.1%	109	$201.20	$150,279	42.4%	$354,515
$300	$1,631.76	$99,364	22.4%	122	$257.47	$140,322	40.7%	$344,559
$400	$1,731.76	$115,583	26.0%	144	$1,037.17	$124,103	37.8%	$328,340
$500	$1,831.76	$128,280	28.9%	161	$580.17	$111,406	35.3%	$315,643

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

Note that the Payoff() function is similar to Payoff2(), except that Payoff() works with a loan starting at the beginning instead of during the payoff lifetime. To see other financial functions, go to the top of this page and click → , or click → . The financial function Refinance() is described below.

Sample 5) Refinancing a loan

Consider a mortgage at 7.375%, with payment of $1,885.66 per month and outstanding balance of $210,420 – what will be the implications of refinancing at 5.125% with a $2,750 refinance charge and taking out an additional $5,000 equity loan?

You can use the Refinance() function. Enter refinance() in the [Expr] box and click to see the arguments. This yields

Function	Args	Results	Prototype/Description	Expr Use?
Refinance	7	table	*Refinance( currBalance, currPayment, currRate, newRate, loanCharge, loanLoan, newDuration* ): Impact (total cost, breakeven, % interest, et cetera) of refinancing a loan: currBalance – Current loan balance (principal) currPayment – Current loan payment (principal and interest components only) currRate – Current loan annual interest rate (percent - e.g., 7.125) newRate – New loan annual interest rate (percent - e.g., 5.75) loanCharge – Addition to principal (loan charge - e.g., closing costs, points) loanLoan – Addition to principal ("equity" payout - may be 0) newDuration – New loan duration (years) Notes: (1) Do not include escrow payments (typically taxes and insurance) with currPayment*, (2) See also Mortgage() and the Payoff() functions	No

The Refinance() function has 7 arguments. Enter the information into the [Expr] box (as below) and click .

Expr

which yields

Refinance(210420, 1885.66, 7.375, 5.125, 2750, 5000, 15);

Balance = $210,420.00 at 7.375% with monthly payments of $1,885.66
Current responsibility = 189 payments (188 * $1,885.66 + $1,809.77)
= $356,313.85 ($145,893.85 = 40.9% is interest)

	Current Mortgage	New Mortgage (w/out Equity)	New Mortgage (w/ Equity)	New Mortgage (Old Payment)
	`------------`	`---------------`	`---------------`	`----------------`
Interest Rate	`7.375%`	`5.125%`	`5.125%`	`5.125%`
Equity "Loan"		`0.00`	`$5,000.00`	`$5,000.00`
Balance	`$210,420.00`	`$213,170.00`	`$218,170.00`	`$218,170.00`
Payment	`$1,885.66`	`$1,699.65`	`$1,739.51`	`$1,885.66`
Last Payment	`$1,809.77`	`$1,699.65`	`$1,739.51`	`$1,710.84`
Months	`189`	`180`	`180`	`160`
Breakeven		`15`	`37`	`22`
Interest	`$145,893.85`	`$92,767.00`	`$94,941.80`	`$83,360.78`
% Interest	`40.9`	`30.3`	`30.8`	`28.1`
	`------------`	`---------------`	`---------------`	`----------------`
Total To Pay	`$356,313.85`	`$305,937.00`	`$308,111.80`	`$296,530.78`
	`------------`	`---------------`	`---------------`	`----------------`
Savings	`—`	`$50,376.85`	`$48,202.05`	`$59,783.06`

This computation is based only on principal and
interest, and assumes no prepayment penalty.
Escrow (taxes + insurance) is not part of the computation.

"Breakeven" is defined as the time (months) from the new mortgage til the current and new balances are the same. This computation is more representative than the simpler (delta dollars)/(delta payment) method, and when the new interest rate is lower than the old rate, will result in a quicker breakeven.
Note that the $5,000.00 equity "loan" with the refinance will end up costing $7,174.80 (that is, $2,174.80 in interest)
The rightmost column represents the "what-if" computation of getting the new loan (5.125%), but continuing to pay it off with the old payment ($1,885.66)

Click Advanced Features to review some of the more advanced ways to use ComputeSoup (also available via → ).