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)
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.
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.
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:
Simply enter calories( in the [Expr] box and
the system will list the arguments and their descriptions for you
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 .
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).
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)
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.
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:
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.
"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)