With most loans in the US, you get what is called an
amortization schedule which shows how
each (monthly) payment gets divided into capital repayment and interest+fees.
The monthly payment is fixed; it is the same amount month after month.
But, the breakdown of the payment into capital repayment and interest
payment differs from month to month as earlier payments are mostly interest
and later payments are mostly capital repayment. This is because each
month the money still owing goes down and so the interest for next
month is less. With a fixed monthly payment, next month's interest is
a little less and capital repayment is a little more. In this scenario,
if the total of the many monthly payments is $X and you borrowed $Y
to start with, then your total cost of borrowing money is simply $(X-Y).
What interest rate did you pay for borrowing the money? It is the APR divided
by 12 per month. That is, if you borrowed $1000 at 6%APR compounded
monthly, then you owe $1000x0.5% = $5 in interest at the end of the
first month. If the loan is for 5 years (60 equal monthly payments), you
pay $19.33 each month. In the first month, you have paid $5 in interest
and reduced the principal due by $14.33 (that is, you owe
only $985.67). So next month you owe only $4.93 = $985.67x0.5%
in interest, but since the monthly payment is still fixed at $19.33, you
get to pay off $14.40 (a tad more than last month's $14.33) of the
amount still outstanding. Lather, rinse and repeat until your
60th payment of $19.33 consists of $19.23 of principal finally being
paid off together with 10 cents interest for that last month on that
$19.23 you still owed. You will have paid $19.33x60 = $1159.80
in monthly payments, that is, $159.80 in interest over the life of
the loan. If you want to think of it as 15.98% interest over 5 years
or a shade under 3.2% per year, feel free to do so. However, most people
won't think of it that way, because they didn't have the use of the
full $1000 for the entire 60 month period. Note that there is no
compounding of interest, that is, you are not charged interest
on previously accrued interest because you are paying off the interest
in full each month.
It is also possible to get interest-only loans where each month you
only pay the interest (and the fees) accrued that month. At the end,
the entire loan amount is due (usually called a balloon payment).
Note that the monthly payment is fixed in this instance too. Thus,
you pay $5 interest each month and at the end of the loan period,
you owe the full $1000 since you have not repaid any part of it.
In fact, your last payment would be $1005 consisting of the
interest for that last month plus the full principal amount. Note that
there is no compounding of interest, that is, you are not
charged interest on previously accrued interest even though there is
no repayment of any part of the principal over the entire life of
the loan.
Hybrids of these two types of arrangement such as "pay the interest and fees
each month plus $20 towards the principal" are also possible. This
would pay off our example loan of $1000 in 50 months instead of 60.
Note that each month's payment would be smaller
than the previous month's payment because the amount of interest
charged each month is decreasing by $20x0.5% = 10 cents each month.
But note that in all these cases, the percentage interest you pay
each month is still the same APR/12. What differs in the three
cases is what the interest is being charged on. And it is all
simple interest, not compound interest, that is charged. The
phrase "6% APR compounded monthly" merely means that you pay 0.5%
per month simple interest on the remaining balance. If it said
"compounded quarterly" and you were making quarterly instead if
monthly payments, you would pay 1.5% per quarter, and it would
still be simple interest each quarter on the remaining balance.
In a different scenario, if you lend money to a bank (this is
usually called a Certificate of Deposit or CD) for 5 years at 6% APR
compounded quarterly (that's what my bank offers instead of monthly
compounding -- your bank might be different), then the interest
is compounded and at the end of 5 years (20 quarters) when the
CD matures, you will get
$1000 x (1 + 0.015)^20 = $1346.86
The compounding has increased the interest that you
have earned from 6% x 5 = 30% to 34.686%
which is 6.136% compounded annually or, if you like to think about
it differently, you got 34.686%/5 = 6.937% simple interest per annum.
(Most everyone else will beg to differ, but whatever makes you comfortable).
This is how CDs work in
the US. In India, CDs are commonly called FDs (Fixed Deposits)
and the interest accrued is paid out quarterly (or monthly
depending on the way it is set up) to the owner;
that is, interest does not accumulate inside the CD as it does
in the US (hence Fixed Deposit), and it is all simple interest:
no compounding since it is all paid out. You would get 1.5% per quarter
($15) for a total of $300 instead of the $346.86 that compounding
would give you (but only after 5 years). But, getting back to the
US, interest earned inside a CD must be declared annually as income
and the bank will include it in the 1099-INT that it sends you
(and the IRS), and you have to pay tax on that money from other
assets or income since you won't have that cash in hand till the
CD matures.
