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Lecture12-Blackboard - Mathematics of Finance Lecture 12...

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Mathematics of Finance Lecture 12
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Interest Rates and Economic Theory Why, when you deposit money in a savings  account, does the bank pay you interest?
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Interest Rates and Economic Theory Why, when you borrow money to purchase a  home, car or holiday, does the lender charge  you interest?
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The Rate of Interest in the Real World Different rates of interest coexist and  fluctuate over time. “Nominal" rate of interest: n r  = r + d + p Real rate of interest “r” Risk premium “d” Expected changes in the price level “p”
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Simple Interest Calculated on the original principal Sum   accrued (aka investment's future value) S = P + P*r*n
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Compound Interest aka "interest on interest“ Most lenders or investors demand that any  interim interest rewards earned over the term  of investment, if not paid when earned, be  treated as an additional investment. Compounded Annually Compounded More than Once Per Year Compounded Continuously
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Interest Compounded Annually Suppose an amount $P is invested for one  year at a rate of r per annum.  The amount  accrued including interest After one year is After two years:    After three years:  After n years:
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Interest Compounded Annually: Example Suppose a principal of $5000 is to be invested at an  annual rate of 15% for five years. What amount is  available on maturity?
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Interest Compounded More than Once Per Year Often interest rates are compounded on a  monthly, weekly or even a daily basis  (although still quoted on an annual basis).
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