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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
omega
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
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
5
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()
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).
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
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 .
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
→
).