http://www.hughchou.org/calc/formula_deriv.html

                              J
         M  =  P  x ------------------------

                      1  - ( 1 + J ) ^ -N

Concept

1. Calculate H = P*J, this is your current monthly interest
2. Calculate C = M – H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for the month.
3. Calculate Q = P – C, this is the new balance of your principal of your loan.
4. Set P = Q and repeat 1.

Definitions

  N  =  No. of months of the mortgage payment
  M  =  Monthly mortgage payment
  J  =  Monthly interest rate
  P  =  Principal

For the first month N = 1 :

  H  =  P*J
  C  =  M - P*J
  Q  =  P - (M - P*J)
     =  P + PJ - M
     =  P(1 + J) - M

For the second month N = 2 :

  H  =  (P(1 + J) - M)*J
  C  =  M - [ PJ(1 + J) - MJ ]
  Q  =  P(1 + J) - M - (M - [ PJ(1 + J) - MJ ])
     =  P(1 + J) - M - M + PJ(1 + J) - MJ
     =  P(1 + J)2 - M(1 + J) - M

For the third month N = 3 :

  H  =  (P(1 + J)2 - M(1 + J) - M)*J
  C  =  M - [PJ(1 + J)2 - MJ(1 + J) - MJ]
  Q  =  P(1 + J)2 - M(1 + J) - M - (M - [PJ(1 + J)2 - MJ(1 + J) - MJ])
     =  P(1 + J)2 + PJ(1 + J)2  - M(1 + J) - MJ(1 + J) - M - MJ - M
     =  P(1 + J)3 - M(1 + J)2 - M(1 + J) - M           [ Equation #1 ]

Let us digress and consider the Geometric series :

We know :

T _n = a rⁿ – 1

so the sum of the series is expressed as

S_n = a [ (1 - rⁿ ) / ( 1 - r ) ]

From [ Equation 1 ] we know that

M(1 + J)² – M(1 + J) – M is a Geometric series.

Where r is (1 + J) and a = M

Thus the sum of this series is equal to

  Sn = M [ (1- (1 + J)n) / (1- (1 + J)) ]      [ Equation #2 ]

Now substitute [ Equation 2 ] into [ Equation 1 ] and set Q = 0,

The reason why we set Q equal to zero is simple, when we finish paying the mortgage Q, the balance is reduced to 0.

So,

  0  =  P(1 + J)N - M [ (1- (1 + J)N) / J) ]
  M  =  J * [ P(1 + J)N / ((1 + J)N - 1) ]
  M  =  PJ * [ (1 + J)N / ((1 + J)N - 1) ]
  M  =  PJ / [ 1 - (1 + J) -N ]

http://jtidy.de/

WordPress has another solution for source code display from code.google.com . It’s excellent but, unfortunately, it does not support ABAP.

Nothing is perfect.

ABAP does an excellent job on UTF-8 file, but may not on UTF-16, depending on your system locale setup. With the help of Google and SAP forum, following code should work on both UTF-8 and UTF-16.

In short, it is composed of detection, parsing and conversion when necessary.

FORM read_unicode USING filename TYPE rlgrap-filename
               CHANGING fileline_tab TYPE string_table.
  DATA: message TYPE string,
        lr_conv TYPE REF TO cl_abap_conv_in_ce,
        lr_ex TYPE REF TO cx_root.

* utf-8
  DATA: file_bom TYPE sychar01,
        file_encoding TYPE sychar01,
        fileline TYPE string.

* utf-16
  DATA: str_utf16 TYPE xstring,
        str_native TYPE string,
        bom(2) TYPE x, "byte order mark for UTF-16
        encoding TYPE abap_encod,
        endian TYPE abap_endia.

  CALL METHOD cl_abap_file_utilities=>check_utf8
    EXPORTING
      file_name = filename
    IMPORTING
      bom       = file_bom
      encoding  = file_encoding.

  IF file_bom EQ cl_abap_file_utilities=>bom_utf8 AND
     file_encoding EQ cl_abap_file_utilities=>encoding_utf8.
*   work as UTF-8
    TRY .
        OPEN DATASET filename FOR INPUT
          IN TEXT MODE
          ENCODING UTF-8 SKIPPING BYTE-ORDER MARK
          WITH SMART LINEFEED.
        IF sy-subrc NE 0.
          WRITE / 'File open failure '.
          RETURN.
        ENDIF.

        DO.
          READ DATASET filename INTO fileline.
          IF sy-subrc NE 0.             "EOF
            EXIT.
          ENDIF.
          APPEND fileline TO fileline_tab.
        ENDDO.

      CATCH cx_root INTO lr_ex.
        message = lr_ex->if_message~get_longtext( ).
        WRITE:/ message.
        CLOSE DATASET filename.
        RETURN.
    ENDTRY.
  ELSE.
*   work as UTF-16
    TRY .
        OPEN DATASET filename FOR INPUT IN BINARY MODE.
        IF sy-subrc NE 0.
          WRITE / 'File open failure'.
          RETURN.
        ENDIF.
        READ DATASET filename INTO str_utf16.
        CLOSE DATASET filename.

      CATCH cx_root INTO lr_ex.
        message = lr_ex->if_message~get_longtext( ).
        WRITE:/ message.
        CLOSE DATASET filename.
        RETURN.
    ENDTRY.

    bom = str_utf16.

    IF bom EQ 'FFFE'.
      encoding = '4103'. "code page for UTF-16LE
      endian = 'L'.
      SHIFT str_utf16 LEFT BY 2 PLACES IN BYTE MODE.  " remove byte-order-mark
    ELSEIF bom EQ 'FEFF'.
      encoding = '4102'. "code page for UTF-16BE
      endian = 'B'.
      SHIFT str_utf16 LEFT BY 2 PLACES IN BYTE MODE.  " remove byte-order-mark
    ELSE.
      WRITE: 'File is neither UTF-8 or UTF-16'.
      RETURN.
    ENDIF.

    TRY.
        CALL METHOD cl_abap_conv_in_ce=>create
          EXPORTING
            encoding    = encoding
            endian      = endian
            replacement = '?'
          RECEIVING
            conv        = lr_conv.

        CALL METHOD lr_conv->convert
          EXPORTING
            input = str_utf16
            n     = -1
          IMPORTING
            data  = str_native.
      CATCH cx_sy_conversion_codepage.
*     replacement occurs automatically. no code is required
      CATCH cx_root INTO lr_ex.
        message = lr_ex->if_message~get_longtext( ).
        WRITE:/ message.
    ENDTRY.

    SPLIT str_native AT cl_abap_char_utilities=>cr_lf INTO TABLE fileline_tab.
  ENDIF.
ENDFORM.                    "read_unicode

Any idea for simpler solution?

To copy to new client:

1) Log on to target client and goto transaction SCC1.
2) Enter the source client and change request number from above.
3) Click the execute button.

Ref: http://sap.ittoolbox.com/documents/popular-q-and-a/copying-variants-from-one-client-to-another-in-sap-1560

Relevant t-codes:
SM36: Create job
SM36WIZ: Create job with wizard
SM37: Job Overview: release scheduled job, display Job logs and steps, etc.
SM21: System Log.
ST22: ABAP runtime error, here it is used to find error info of background program
SP02: Display background report output which is outputed by WRITE statement.

Relevant FMs:
1. JOB_OPEN: Define a job
2. JOB_SUBMIT: Append program, external command or external program to the job.
=>Job Status: “Scheduled”.
3. JOB_CLOSE: Release a job. You can let the job run immediately, or run in specific start data & time, or after which event or job.
=>Job Status: “Released”
4. SHOW_JOBSTATE: Get job status
5. BP_JOBLOG_READ: Read job log into an itab

Useful FMs in Function Group: BTCH

Src: http://sap.group.javaeye.com/group/blog/127587