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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 20 "Mortgage Calculation" }}{PARA 
19 "" 0 "" {TEXT -1 17 "Jeremy R. Johnson" }}{PARA 0 "" 0 "" {TEXT -1 
94 "Determining the monthly loan payment given the principle, interest
 rate, and term of the loan." }}{PARA 0 "" 0 "" {TEXT -1 117 "Let P = \+
principle, r = rate (compounded each payment period), t = term (number
 of payments), and M = monthly payment." }}{PARA 0 "" 0 "" {TEXT -1 
64 "We derive an equation for the updated principle after t payments" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "P[0] := P;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#\"\"!F%" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "P[1] := P*(1 + r) - M;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#\"\"\",&*&F%F',&F'F'%\"rGF'F
'F'%\"MG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "P[2] := P[
1]*(1 + r) - M;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#\"\"#,&*&,
&*&F%\"\"\",&F,F,%\"rGF,F,F,%\"MG!\"\"F,F-F,F,F/F0" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "collect(%,P);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(*&),&\"\"\"F'%\"rGF'\"\"#F'%\"PGF'F'*&%\"MGF'F&F'!\"\"F,F-" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "P[3] := P[2]*(1+r) - M;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#\"\"$,&*&,&*&,&*&F%\"\"\",&F.
F.%\"rGF.F.F.%\"MG!\"\"F.F/F.F.F1F2F.F/F.F.F1F2" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "collect(%,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,(*&),&\"\"\"F'%\"rGF'\"\"$F'%\"PGF'F'*&,&*&%\"MGF'F&F'!\"\"F.F/F'F
&F'F'F.F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "P[4] := %*(1+r
) - M;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"PG6#\"\"%,&*&,(*&),&\"
\"\"F.%\"rGF.\"\"$F.F%F.F.*&,&*&%\"MGF.F-F.!\"\"F4F5F.F-F.F.F4F5F.F-F.
F.F4F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "collect(%,P);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&),&\"\"\"F'%\"rGF'\"\"%F'%\"PGF'F'
*&,&*&,&*&%\"MGF'F&F'!\"\"F0F1F'F&F'F'F0F1F'F&F'F'F0F1" }}}{PARA 0 "" 
0 "" {TEXT -1 40 "After t payments this can be written as " }{XPPEDIT 
18 0 "P*(1+r)^t - M*Sum((1+r)^i,i=0..t-1)" "6#,&*&%\"PG\"\"\"),&F&F&%
\"rGF&%\"tGF&F&*&%\"MGF&-%$SumG6$),&F&F&F)F&%\"iG/F2;\"\"!,&F*F&F&!\"
\"F&F7" }{TEXT -1 44 ".  Setting this equation to zero and solving" }}
{PARA 0 "" 0 "" {TEXT -1 32 "for M gives the monthly payment." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "# Interest Equation" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "# Inputs
:  " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#   P : Principle" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 52 "#   r : interest rate (compounded every t
ime period)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "#   t : number of ti
me periods" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "# Output:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 76 "#   An equation for determining the payment \+
amount (M) for each time period." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 
"#   set the equation equal to 0 and solve for M." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 26 "IE := proc(P,r,t) local i;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "P*(1+r)^t - M*sum((1+r)^'i','i'=0..t-1);" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IE
Gf*6%%\"PG%\"rG%\"tG6#%\"iG6\"F,,&*&9$\"\"\"),&F0F09%F09&F0F0*&%\"MGF0
-%$sumG6$)F2.8$/F;;\"\"!,&F4F0F0!\"\"F0FAF,F,F," }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "IE(P,r,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,&*&%\"PG\"\"\"),&F&F&%\"rGF&%\"tGF&F&*&%\"MGF&,&*&F'F&F)!\"\"F&*&F&F&
F)F/F/F&F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(%,M);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%\"PG\"\"\"),&F%F%%\"rGF%%\"tGF%F(
F%,&F&F%F%!\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "paymen
t := unapply(%,P,r,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(paymentGf
*6%%\"PG%\"rG%\"tG6\"6$%)operatorG%&arrowGF***9$\"\"\"),&F0F09%F09&F0F
3F0,&F1F0F0!\"\"F6F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"total := payment(P,r,t)*t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tota
lG*,%\"PG\"\"\"),&F'F'%\"rGF'%\"tGF'F*F',&F(F'F'!\"\"F-F+F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "IE(30000,.0874/12,12*9);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+!f***ol!\"&\"\"\"*&$\"+)\\4Mj\"!
\"(F'%\"MGF'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(
%,M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+[*[;-%!\"(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to 15 do" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "IE(30000,.0874/12,12*i);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "monthly[i] := solve(%,M);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "total[i] := 12*i*monthly[i];" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+1D'HF$!\"
&\"\"\"*&$\"+!Qc#\\7!\")F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%(monthlyG6#\"\"\"$\"+!fG*>E!\"'" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%&totalG6#\"\"\"$\"+3V\"R9$!\"&" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&$\"+!>h2d$!\"&\"\"\"*&$\"+y%z@h#!\")F'%\"MGF'!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"\"#$\"+_i'pO\"!\"'" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"\"#$\"+0!>2G$!\"&" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,&$\"+Kel&*Q!\"&\"\"\"*&$\"+V:6*4%!\")F'%\"MGF'
!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"\"$$\"+.!fO]*
!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"\"$$\"+TsJ@M!\"&
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+E=6]U!\"&\"\"\"*&$\"+WeL@d!
\")F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"
\"%$\"+x0`Gu!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"\"%$
\"+xYplN!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+&))=oj%!\"&\"\"
\"*&$\"+#Gi6\\(!\")F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
&%(monthlyG6#\"\"&$\"+7*=(*='!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
&%&totalG6#\"\"&$\"+Z8$Qr$!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$
\"+`9re]!\"&\"\"\"*&$\"+13-A%*!\")F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%(monthlyG6#\"\"'$\"+H-.p`!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%&totalG6#\"\"'$\"+k<qlQ!\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&$\"+r4**=b!\"&\"\"\"*&$\"+Kj&G:\"!\"(F'%\"MGF'!\"\"" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"\"($\"+9AB(y%!\"(" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"\"($\"+g]F@S!\"&" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+u,:@g!\"&\"\"\"*&$\"+*[xEQ\"!\"(
F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"\")$
\"+kKqaV!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"\")$\"+L
^^!=%!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+!f***ol!\"&\"\"\"*&
$\"+)\\4Mj\"!\"(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(
monthlyG6#\"\"*$\"+[*[;-%!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&t
otalG6#\"\"*$\"+k3QVV!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+akp
mr!\"&\"\"\"*&$\"+')\\&p!>!\"(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%(monthlyG6#\"#5$\"+#e)=eP!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%&totalG6#\"#5$\"+)HE)4X!\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&$\"+iix=y!\"&\"\"\"*&$\"+&p*Q0A!\"(F'%\"MGF'!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"#6$\"+2PIXN!\"(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"#6$\"+%*3!)zY!\"&" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+%=(=I&)!\"&\"\"\"*&$\"+K#y4`#!\"
(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(monthlyG6#\"#7$
\"+YBJqL!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG6#\"#7$\"+y(
\\K&[!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+4wK1$*!\"&\"\"\"*&$
\"+e7>')G!\"(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(mon
thlyG6#\"#8$\"+b?VCK!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&totalG
6#\"#8$\"+1S6I]!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&$\"+6(3`,\"!
\"%\"\"\"*&$\"+HUstK!\"(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%(monthlyG6#\"#9$\"+6uQ,J!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>&%&totalG6#\"#9$\"+]3L5_!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&
$\"+:\"*o26!\"%\"\"\"*&$\"+dy^'p$!\"(F'%\"MGF'!\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%(monthlyG6#\"#:$\"++Xd'*H!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%&totalG6#\"#:$\"++T$QR&!\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "for i from 1 to 15 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "  payment(30000,.0874/12,12*i);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+:(G*>E!\"'
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+9j'pO\"!\"'" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"+I%fO]*!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
+44`Gu!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*=>(*='!\"(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+s/.p`!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+JCB(y%!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+l
MqaV!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+K\"\\;-%!\"(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+`()=eP!\"(" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+qQIXN!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++DJqL!\"(" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+.AVCK!\"(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+_vQ,J!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+PY
d'*H!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to
 15 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "  interest[i] := total[i]
 - 30000;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"\"$\"*3V\"R9!\"&" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>&%)interestG6#\"\"#$\"*0!>2G!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"$$\"*TsJ@%!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"%$\"*xYpl&!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"&$\"*Z8$Qr!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"'$\"*k<ql)!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\"($\"+g]F@5!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"\")$\"+L^^!=\"!\"&" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>&%)interestG6#\"\"*$\"+k3QV8!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"#5$\"+)HE)4:!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"#6$\"+%*3!)z;!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"#7$\"+y(\\K&=!\"&" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%)interestG6#\"#8$\"+1S6I?!\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%)interestG6#\"#9$\"+]3L5A!\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%)interestG6#\"#:$\"++T$QR#!\"&" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "pointplot([seq([i,monthly[i]],i=1..15)]);" }}{PARA 
13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6#-%'POINTSG617$$\"\"\"
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{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6#-%'POINTSG617$$
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nterest[14])*t-interest[15]*14+interest[14]*15,t=1..15):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(\{p1,p2\});" }}{PARA 13 "" 
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