CrunchJr – Overview

CrunchJr is a powerful computational engine.  Two basic forms of operation are supported (Quick–mode and PowerUser–mode), and users can move back and forth at any time.  Quick–mode is well suited to first time users, and many users end up using it as their main form of interaction.  PowerUser–mode is much more flexible and powerful.

  Quick–mode  

Quick–mode presents 250+ MiniApps grouped into 36 domains (including Health/Fitness, Dollars/Sense, Solvers, Date Computations, Geometry, General Math, Physics, ...).  Some MiniApps appear in more than one domain.  Tapping [MiniApps] → {Dollars/Sense} offers 12 MiniApps.  You can choose simple apps (e.g., Bill Split, Present Value or Price Per).  Each will ask you for a couple of parameters then present the results in an easy-to-read format.  Or, you may choose more complex MiniApps like Refinance which outlines the impact of refinancing a mortgage, or Payoff Strategy, which displays the long-term savings of paying an extra amount with each monthly mortgage payment.

Similarly, [MiniApp] → {Health/Fitness} presents 9 MiniApps – including Calories (present the calories burned for any of 38 workouts as a function of weight, time, distance), BMI (Body Mass Index), Race Pace, Race Time (compute workout/race times and paces), and Heart Rate (lays out target heartrates based on age, condition, intensity).

  PowerUser–mode  

PowerUser–mode includes all the features described above and much more. It allows users to evaluate expressions (including those which have variables – each with one or more values), and displays the results in easy-to-read tables.  Many standard mathematical constants and functions are available for use in the expressions, as well as a collection of special purpose functions which support a wide variety of computational needs, for example various physics computations, solving cubic and quartic equations, refinance and mortgage payoff strategies, simple matrix manipulations, and complex number arithmetic.  Tapping the Inputs tab leads to detailed information about the hundreds of available Functions and Constants, as well as opportunities to review your computational History, see and modify your stored Variables and their values, and check on your individual User-defined Functions. Data from these sources may be useful in building your computations.  There are several advanced features, including storing results for later use, personalizing your environment, integration, building user-defined functions, auto expansion while you type, and input shortcuts.

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 PowerUser–mode samples (tap a number to jump to the sample). 

  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
       (Home)

    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 tap .

 

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

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 

OpCount:    558
CP-Time:    33µsec

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).  For this example, the ShowOpCount option has been turned on, and the operation count and CPU time are displayed.  The nine result values of tr are automatically saved in the Store.   If you use tr in a subsequent computation during this or another 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 list       →  (Home)        

    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, seconds).  It shows the time to cover the distance at the input pace.  Enter the information into the [Expr] box and tap .

 

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.

 

Enter value(s) for xmin and tap .
xmin  



which yields
Dist (mi) TimePace
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 list       →  (Home)        

    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.  Either of these 2 steps can help you with the arguments:
  1. Simply enter calories( in the [Expr] box and the system will list the arguments and their descriptions for you
  2. Tap [Inputs] → {Functions} → Calories to see the arguments (and descriptions); tapping the Use button will place the function in the [Expr] box for you
For example, enter the argument values into the [Expr] box (as below) and tap .

 

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.  There are a total of 38 activities to choose from, for example, running, swimming, tennis, walking, aerobics, ....

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

 

which yields

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

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

 

which yields

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

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

→  Sample list       →  (Home)        

    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.  Use any of the techniques above to see the arguments, then enter the information into the [Expr] box (as below) and tap .

 

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).  (334 months = 27 years, 10 months)

An extra $200/month saves $77,785 (17.5%),  pays off loan 94 months (7y 10m) 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:

 

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 tap , then enter the additional amount(s) to pay for each month (values for add) and tap 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).  (334 months = 27 years, 10 months)

MonthlyMonthly/----------- Saves ----------\FinalTotalTotal
ExtraPayment$%Months PaymentInterestPayments
 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.
→  Sample list       →  (Home)        

    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.  Gathering the prototype (as described in Sample 3) yields:
Refinance( currBalance, currPayment, currRate, newRate, loanCharge, loanLoan, newDuration )
Enter the information (7 arguments) into the [Expr] box (as below) and tap .

 

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).  (189 months = 15 years, 9 months)


    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.

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