Monthly interest - 12th root or 1/12?
jgharston
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?
TR Oltrogge
"jgharston" <j...@arcade.demon.co.uk> wrote in message
news:6d0865b5-de2f-4a34...@p25g2000pri.googlegroups.com...
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.
Barb Knox
<6d0865b5-de2f-4a34...@p25g2000pri.googlegroups.com>,
jgharston <j...@arcade.demon.co.uk> wrote:
In consumer law, "APR" is *defined* to be the monthly interest rate * 12.
It thus differs from the true effective annual interest rate, which as
you correctly imply is ((1+monthlyRate/100)^12)*100-100.
Thus the "APR" systematically understates the true annual interest rate,
which is nice for the lenders. Also, most borrowers wouldn't understand
an exponential.
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