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Lecture 7

# Lecture 7 - Recall the importance of interest rates they...

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Recall the importance of interest rates they determine the time value of money. A dollar today is not worth a dollar in the future, even without any inflation! Remember that the cost of something is what must be given up in order to get it. To get a dollar in one year I don't need to give up a dollar today, not when I can put about 97 cents into the bank and, with 3% interest, get \$1 in a year's time. Generally we use continuously-compounded interest, so that an amount invested at a fixed interest rate grows exponentially. Unless you've read the really fine print at the bottom of some loan document, you probably haven't given much thought to the differences between the various sorts of compounding annual, semi-annual, etc. If \$1 is invested and grows at rate R then annual compounding means I'll have (1 + R) after one year. If \$1 is invested and grows at rate R then semi-annual compounding means I'll have after one year. " compounding 3 times means I'll have after one year. " compounding m times means I'll have after one year. " continuous compounding (i.e. letting ) means I'll have e R after one year. And note that sometimes we write e R ; sometimes exp{R} if the stuff buried in the superscript is important enough to get the full font size. You might hope that that would be enough, but it's not. The real world is complicated so there are lots of different ways to measure interest! This class will usually think of it in the mathematically convenient continuous form, and use all of the rest of the definitions to translate. If the interest is only compounded once per year, then the present value of some amount of

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Lecture 7 - Recall the importance of interest rates they...

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