| Interest is the fee paid on borrowed money. The
lender receives a compensation for foregoing other uses of their
funds, including (for example) deferring their own consumption.
The original amount lent is called the "principal,"
and the percentage of the principal which is paid/payable over
a period of time is the "interest rate."
Types of interest
Simple Interest
Simple interest does not take compounding into account, and
is determined by multiplying the principal by the interest rate
(per period) by the number of time periods. |
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To calculate: Add up all the interest paid/payable
in a period. Divide that by the principal at the beginning of
the period. E.g. on $100 (principal):
- credit card debt where $1/day is charged. 1/100 = 1%/day.
- corporate bond where $3 is due after six months, and another
$3 is due at year end. (3+3)/100 = 6%/year.
- certificate of deposit (GIC) where $6 is paid at year end.
6/100 = 6%/year.
There are three problems with simple interest.
- The time periods used for measurement can be different, making
comparisons wrong. You cannot say the 1%/day credit card interest
is 'equal' to a 365%/year GIC.
- The time value of money means that $3 paid every six months
hurts more than $6 paid only at year end. So you cannot 'equate'
the 6% bond to the 6% GIC.
- When interest is due, but not paid, it must be clear what
happens. Does it remain 'interest payable', like the bond's
$3 payment after six months? Or does it get added to the original
principal, like the 1%/day on the credit card? Each time it
is added to the principal it 'compounds'. The interest from
that time forward is calculated on that (now larger) principal.
The more frequent the compounding, the faster the principal
grows, and the greater the interest amount is.
To find the simple interest = C= prt. (p=principle) (r=rate)
(t=time) (c=simple interest). (Ex. 2,3000 * 5.3246 * 5 = simple
interest.
Compound Interest
In order to solve these three problems, there is a convention
in economics that interest rates will be disclosed as if the term
is one year and the compounding is yearly, otherwise known as
the effective interest rate. The discussion at compound interest
shows how to convert to and from the different measures of interest.
Interest rates in lending are often quoted as nominal interest
rates (compounding interest uncorrected for the frequency of compounding.
Loans often include various non-interest charges and fees (such
as points on a mortgage loan in the United States; many jurisdictions
require lenders to provide information on the 'true' cost of finance,
often expressed as an annual percentage rate, which expresses
the total cost of a loan as an interest rate after including the
additional fees and expenses (the details, however, vary). In
economics, continuous compounding is often used due to specific
mathematical properties.
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