The total interest earned is 3192 100 3092 the simple

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The total interest earned is $3,192 - $100 = $3,092. The simple interest earned is $100*45*0.08 = $360. Therefore the compound interest (interest on interest on interest) is $3,092 - $360 = $2,732 Alternatively, we could have calculated the interest on interest as H I o I = $3,192 - $460 = $2,732 4
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iClicker Example: Compound Interest H Suppose you invest $1000. The effective annual interest rate is 8%. At the beginning of year 5, you take all the money out of the account to buy a new TV. How much money can you spend? a) $1,360.49 b) $1,469.33 c) $1,215.51 d) $1,276.28 e) $1,360.50 Answer: a) $1,360.49 (note on rounding) Timeline: 0 1 2 3 4 5 Period -----|------|------|------|------|------|-------- $1000 FV 4 = ? 5
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Example: The Manhattan Purchase H Native Americans allegedly sold Manhattan to the British for $24 in 1626. Had they invested this money at an annual rate of return of 7.2%, what would the money have grown to in 1999? H What is n? 1999 -1626 = 373 H Then: FV 1999 = $24*(1+0.072) 373 = $4.4 trillion (12 0s) According to Case (2000), the aggregate value of all residential real estate in the US was about $11.6 trillion at the end of 1999 . What would it have been worth at the end of 2009? H n = 2009 – 1626 = 383 H Then: FV 2009 = $24*(1+0.072) 383 = 8.88 trillion Note that the value doubled over 10 years. » Compound interest -> investments grow exponentially 6
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Aside: The Rule of 72 H For interest rate between, say, 5%-20%, money doubles in approximately years In our last example, this would have been years. => For r = 7.2%, Rule of 72 works exactly. r 72 10 2 . 7 72 72 = = r 7
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General Present Value Formula H Second Rule of Time Travel H In Finance, we often have to find today s value of (more or less certain) future cash flows. Said differently, we have to look for a present value. H From H We can easily get: n n r PV FV ) 1 ( * + = PV t = 0 = FV n (1 + r ) n = FV n * 1 (1 + r ) n = FV n * 1 1 + r !
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