Incurring
debt and making a series of payments to reduce this debt to nil is something
we all must do in our lifetime as we make purchases that would only be
feasible if we are given sufficient time to pay down the amount of the
transaction.
This is referred to as 'amortizing' a debt, a term that takes it's roots
from the French term ' amortir', which is the act of providing death to
something.
The basic definitions required for someone to understand the concept are:
1. Principal  the initial amount of the debt, usually
the price of the item purchased.
2. Interest Rate  the amount one will pay for the use
of someone else's money. Usually expressed as a percentage so that this
amount can be expressed for any period of time.
3. Time essentially the amount of time that will be
taken to pay down (eliminate) the debt. Usually expressed in years, but
best understood as the number of and interval of payments, i.e., 36 monthly
payments.
Simple interest calculation follows the formula:
I= PRT, where
I=Interest
P=Principal
R= Interest Rate
T= Time.
The challenge:
John decides to buy a car. The dealer gives him a price and tells him
he can pay on time as long as he makes 36 installments and agrees to pay
six per cent interest. (6%). The facts are:
Agreed price
18,000 for the car, taxes included.
3 years or
36 equal payments to pay out the debt.
Interest
rate of 6%.
The first payment will occur 30 days after receiving the loan
A simple timeline will give you an idea of the question we need to address.
. To simplify the problem, we know the following:
1. The monthly
payment will include at least 1/36th of the principal so we can pay off
the original debt.
2. The monthly payment will also include an interest component that is
equal to 1/36 of the total interest.
3. Total interest is calculated by looking at a series of varying amounts
at a fixed interest rate.
Take a look
at this chart reflecting our loan scenario.
This picture
shows the calculation of interest for each month, reflecting the declining
balance outstanding due to the principal pay down each month . ( 1/36
of the balance outstanding at the time of the first payment.,., in our
example 18,090/36 = 502.50)
By totaling the amount of interest and calculating the average, you can
arrive at a simple estimation of the payment required to amortize this
debt. Averaging will differ from exact because you are paying less than
the actual calculated amount of interest for the early payments, which
would change the amount of the outstanding balance and therefore the amount
of interest calculated for the next period.
Understanding the simple effect of interest on an amount in terms of a
a given time period and realizing that amortization is nothing more then
a progressive summary of a series of simple monthly debt calculations
should provide a person with a better understanding of loans and mortgages.
The math is both simple and complex; calculating the periodic interest
is simple but finding the exact periodic payment to amortize the debt
is complex.
Watch for
more Business Math articles....
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