ORIE 3150
October 1, 2009
Interest is the cost of borrowing money or the return from lending money.
If you lend
someone $5 today and you receive $6 one year from now, the difference of $1 represents
the interest paid on the account borrowed.
Interest rates are usually stated as annual percentage rates.
If you borrow $100 from the
bank at 6% per annum (per year), you must pay the bank $100 + $6 (with the $6 coming
from the calculation $6 = 0.06 × $100) or a total of $106 at the end of the year.
The interest rate applicable in an economic transaction is affected by the perceived risk or
probability of non-payment in the transaction.
A bank may lend money to a low risk
customer at 7.5%, but a high risk person may have to borrow money at the pawn shop at
36% or more.
Simple Interest
.
Simple interest is interest earned only on the original principal.
The formula for
calculating simple interest is
n
i
P
I
×
×
=
Where I = simple interest
P = principal (amount borrowed or lent)
i = interest rate per year
n = number of years or fraction thereof
Simple interest is not used too often in business.
It is used for short term notes and for
some bank loans.
Most of the time, compound interest is used.
Compound Interest
Compound interest is interest that is earned on both principal and interest.
When interest
is compounded, interest is earned on the original principal and on the interest
accumulated for the preceding periods.
Ex.
You borrow $500 on January 1, 2000 at 10% interest, compounded annually.
You
pay the loan on Dec. 31, 2004.
What will your total payment be?
Year
Principal
Interest
Total Payoff at End of Year
2000
$500.00
$50.00
$550.00
2001
550.00
55.00
605.00
2002
605.00
60.50
665.50
2003
665.50
66.55
732.05
2004
732.05
73.21
805.26
Answer:
You must pay $805.26

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*Sign up*Interest can be compounded continuously, daily, monthly, quarterly, or semi-annually, or
annually.
We will focus on the latter four.
Present and Future Value of Single Amounts

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