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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 30 "Installment Loan Calcul
ations " }{TEXT -1 26 "(Mortgage, Car Loan, etc.)" }}{PARA 257 "" 0 "
" {TEXT -1 43 "Initial Version:  Earl C. Swallow  11/23/98" }}{PARA 
258 "" 0 "" {TEXT -1 44 "Revised with added comments:  ECS   10/10/99
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "This \+
is a simple illustration of using Maple to do a simple installment loa
n calculation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 "TL = Total Loan Amount  (
can set this to $1000 and then scale from there)" }}{PARA 0 "" 0 "" 
{TEXT -1 19 "RY = interest rate " }{TEXT 257 8 "per year" }}{PARA 0 "
" 0 "" {TEXT -1 78 "NPY = number of payment periods per year (12, if p
ayment period is one month) " }}{PARA 0 "" 0 "" {TEXT -1 45 "r = inter
est rate per payment period = RY/NPY" }}{PARA 0 "" 0 "" {TEXT -1 52 "p
p = payment per payment period (per month, usually)" }}{PARA 0 "" 0 "
" {TEXT -1 42 "NY = total number of years for loan payoff" }}{PARA 0 "
" 0 "" {TEXT -1 54 "NPT = total number of periods for loan payoff = NY
*NPY" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "T
he formula for the payment per payment period (from summation of a bin
omial series) is " }{XPPEDIT 18 0 "pp = TL*r/(1-(1 + r)^(-NPT))" "/%#p
pG*(%#TLG\"\"\"%\"rGF&,&F&F&),&F&F&F'F&,$%$NPTG!\"\"F-F-" }{TEXT -1 2 
" ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "First calculate at 6.9% for 3 ye
ars with a nominal $1000 loan." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "TL := 10
00.00;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "RY := 0.069;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "NPY := 12;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "r := RY/NPY;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "NY := 3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "NPT := NPY*NY;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Next comput
e the payment per period (month):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "pp := TL*r/(1-(1 + r)^(-NPT));" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 46 "Thus, the monthly payment for $16,000 loan is " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "pp*16;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "TotalPaid := NPT*pp;" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 30 "InterestPaid = TotalPaid - TL;" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 36 "Check the calculation: we know that " }{TEXT 
258 18 "pp = TotalPaid/NPT" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "(TotalPaid/NPT);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 14 "It looks good." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 72 "                                     ----
-------------------------------" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 35 "Next calculate at 1.9% for 3 years." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "TL := 1000.00;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "RY := 0.019;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "NPY := 12;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "r := RY/NPY;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "NY := 3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "NPT := NPY
*NY;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Next compute the payment \+
per period (month):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "pp :
= TL*r/(1-(1 + r)^(-NPT));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Thu
s, the monthly payment for $16,000 loan is " }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 6 "pp*16;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "TotalPaid := NPT*pp;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 
"InterestPaid = TotalPaid - TL;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
36 "Check the calculation: we know that " }{TEXT 259 18 "pp = TotalPai
d/NPT" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(T
otalPaid/NPT);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "So, 1.9% for 3 years
 saves $109.93 - $29.56 = $80.37 for each $1000 borrowed." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "For $16,000 borrow
ed, the savings is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "16*80
.37;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 3 0" 0 }
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