[ww-bugs] Bug 3611: New: Are the number of periods off by a factor of 2

[bugzilla-daemon at webwork.maa.org]

http://bugs.webwork.maa.org/show_bug.cgi?id=3611

           Summary: Are the number of periods off by a factor of 2
           Product: Problem Libraries
           Version: unspecified
          Platform: PC
               URL: /opt/webwork/courses/452_Spring_2016/templates/Library
                    /NAU/setExponentialModeling/bonds2.pg_with_problemSeed
                    =2843
        OS/Version: Windows
            Status: NEW
          Severity: normal
          Priority: P5
         Component: Library (OPL)
        AssignedTo: jj at asu.edu
        ReportedBy: travis at mc.edu
        Web browser ---
           version:


Since this bond has coupons paid semiannually then it seems to me that there
are twice as many periods to consider when determining the value of the coupon
portion when setting selling price (ie. annuity formula).  Further, when
determining the present value of the bond Maturity Value, you can either
presume half the nominal rate for twice the periods or the annual rate for the
given number of periods but not both.  Perhaps I am reading this wrong or just
don't understand bond pricing. However, my suggestion:

# If determining value using compounding twice a year (suggested)
$n2 = 2*$n;
$fact1 = ( 1 - (1 + $r2/200 ) ** -$n2 ) / ( $r2/200 );
$P1 = ( $F * ( 1 + $r2/200 ) ** -$n2 ) + ($F * ( $r1/200 ) * $fact1 );

$fact2 = ( 1 - (1 + $r3/200 ) ** -$n2 ) / ( $r3/200 );
$P2 = ( $F * ( 1 + $r3/200 ) ** -$n2 ) + ($F * ( $r1/200 ) * $fact2 );

$fact3 = ( 1 - (1 + $r4/200 ) ** -$n2 ) / ( $r4/200 );
$P3 = ( $F * ( 1 + $r4/200 ) ** -$n2 ) + ($F * ( $r1/200 ) * $fact3 );

# If determining value using compounding once a year (and ignoring time effect
for the six-month coupon..not suggested)
$fact1 = ( 1 - (1 + $r2/100 ) ** -$n ) / ( $r2/200 );
$P1 = ( $F * ( 1 + $r2/100 ) ** -$n ) + ($F * ( $r1/100 ) * $fact1 );

$fact2 = ( 1 - (1 + $r3/100 ) ** -$n ) / ( $r3/200 );
$P2 = ( $F * ( 1 + $r3/100 ) ** -$n ) + ($F * ( $r1/100 ) * $fact2 );

$fact3 = ( 1 - (1 + $r4/100 ) ** -$n ) / ( $r4/100 );
$P3 = ( $F * ( 1 + $r4/100 ) ** -$n ) + ($F * ( $r1/100 ) * $fact3 );

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