"jgharston" <jgh@[EMAIL PROTECTED]
> wrote in message
news:6d0865b5-de2f-4a34-9b1f-6e20353ff353@[EMAIL PROTECTED]
> Back in school 30-odd years ago I was taught that monthly
> interest on a loan/investment is the 12th root of the annual
> interest, ie: loan=loan*((1+apr/100)^(1/12)).
>
> Doing a bit of checking for some source code I find
> everybody saying that monthly interest is 1/12 of the
> annual interest, ie: loan=loan*((1+apr/100)/12).
>
> Checking my mortgage statement shows my bank using
> 1/12 not root12. Has something changed in the last 30
> years? Can banks not work out 12th roots any more, or
> were my teachers wrong?
Nothing's changed as far as I know. I haven't had a mortgage in 20 years
so
I can't check bank statements. But they always quote you an annual rate of
interest, say 6.0%. Then each month they charge interest equal to 0.06/12
times your outstanding balance. No 12th root, just division by 12. Then
they
apply your payment against this slightly increased balance to wipe out the
interest *and* some of the prinicipal.
Let's say your outstanding balance on January 1st (before the interest
calculation and your payment is applied) is $100,000 and you pay $800 each
month. The bank charges you 0.06/12*$100000=$500 interest at 12:00AM and
then applies your $800 payment you make later in the day. You now owe
$100000+$500-$800=$99700.
On February 1st they charge you 0.06/12*$99700=$498.50 interest at 12:00AM
and then applies your $800 payment later in the day. Tou now owe
$99700+$498.50-$800=$99398.50.
Now, if you got lazy and didn't pay your monthly $800 for a whole year
(and
they didn't foreclose on you) your outstanding balance would grow to be
(1+0.06/12)^12 because the interest they add at 12:00AM at the beginning
of
every month gets added to the outstanding balance and thus is being
"compounded". At the end of the year you would owe $106167.78, which is
slightly larger than 6.0% because of the compounding.
So now you can use your formula that an *ANNUAL PERCENTAGE RATE* of
6.16778%
can be equated to its equivalent monthly rate by (1+6.16778/100)^(1/12),
or
1.005, or 0.5% monthly, or 6.0% yearly.
|
