[Kc] solving for interest rate

[David Nicol]

If anyone is considering paying in advance for Linode virtual servers,
the one-year discount is a better deal than the two-year.



$  perl r-solver12 15 24
15% discount on $24 is $20.4
 a 15% discount for 24 payment at a time implies an r of 0.174889697023665

MONTH PRINCIPAL-BEFORE PAYMENT PRINCIPAL-AFTER
    0          20.4000 ( 1.00)         19.4000
    1          19.6848 ( 1.00)         18.6848
    2          18.9591 ( 1.00)         17.9591
    3          18.2228 ( 1.00)         17.2228
    4          17.4756 ( 1.00)         16.4756
    5          16.7175 ( 1.00)         15.7175
    6          15.9482 ( 1.00)         14.9482
    7          15.1677 ( 1.00)         14.1677
    8          14.3757 ( 1.00)         13.3757
    9          13.5721 ( 1.00)         12.5721
   10          12.7566 ( 1.00)         11.7566
   11          11.9292 ( 1.00)         10.9292
   12          11.0897 ( 1.00)         10.0897
   13          10.2378 ( 1.00)          9.2378
   14           9.3734 ( 1.00)          8.3734
   15           8.4963 ( 1.00)          7.4963
   16           7.6064 ( 1.00)          6.6064
   17           6.7034 ( 1.00)          5.7034
   18           5.7871 ( 1.00)          4.7871
   19           4.8574 ( 1.00)          3.8574
   20           3.9140 ( 1.00)          2.9140
   21           2.9568 ( 1.00)          1.9568
   22           1.9855 ( 1.00)          0.9855
   23           1.0000 ( 1.00)         -0.0000

$  perl r-solver12 10 12
10% discount on $12 is $10.8
 a 10% discount for 12 payment at a time implies an r of 0.234854609283606

MONTH PRINCIPAL-BEFORE PAYMENT PRINCIPAL-AFTER
    0          10.8000 ( 1.00)          9.8000
    1           9.9937 ( 1.00)          8.9937
    2           9.1714 ( 1.00)          8.1714
    3           8.3329 ( 1.00)          7.3329
    4           7.4779 ( 1.00)          6.4779
    5           6.6059 ( 1.00)          5.6059
    6           5.7167 ( 1.00)          4.7167
    7           4.8099 ( 1.00)          3.8099
    8           3.8852 ( 1.00)          2.8852
    9           2.9422 ( 1.00)          1.9422
   10           1.9806 ( 1.00)          0.9806
   11           1.0000 ( 1.00)          0.0000
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