Lecture 10 0227

# Lecture 10 0227 - ORIE 350 Time Value of Money Time Value...

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ORIE 350 February 27, 2007 Time Value of Money

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Time Value of Money 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 amount borrowed. Interest rates are usually stated as annual rates. If you borrow \$100 from the bank at 6% per annum (per year), payable in one year, you must pay the bank \$100 + \$6 (0.06 × \$100) or a total of \$106 at the end of the year.
Interest Rates 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.

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An interest rate has three components: 1. A risk-free component based on an economic concept called the marginal productivity of capital. Many economists believe this rate is about 3 or 4 percent in a risk-free and inflation free environment. 2. A risk component to compensate for uncertainty or the possibility of nonpayment. 3. An inflation component applicable in periods of inflation. In periods of inflation, lenders demand higher rates of return to compensate for the decline in purchasing power between the time money is lent and the time it is paid.
Simple Interest Simple interest is interest earned only on the original principal. The formula for calculating simple interest is I = P×i×n I = simple interest P = principal (amount borrowed or lent) i = interest rate per year n = number of years or fraction thereof

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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. This is used for home mortgages, car loans, credit cards, and many (but not all) commercial loans.
Example 1 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?

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