7.01_econ_2 - Types of cash flow $100 $70 Irregular(mixed...

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1    © M Pore  -  7.01  -  econ 2.ppt Types of cash flow 0 2 1 3 4 5 years Irregular (mixed) series:   $70 $100 $80 $50 $80 0 2 1 3 4 5 years $100 $100 $100 $100 $100 $110 $110 $110 $110 $110 6 8 7 9 10
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2    © M Pore  -  7.01  -  econ 2.ppt Exercise your understanding What value of c makes the two diagrams equivalent, when i = 8%? 0 2 1 3 4 5 years $70 $100 $80 $50 $80 0 2 1 3 4 5 years c c c c c
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3    © M Pore  -  7.01  -  econ 2.ppt Exercise your understanding What value of c makes the two diagrams equivalent, when i = 8%? 0 2 1 3 4 5 years $70 $100 $80 $50 $80 0 2 1 3 4 5 years c c c c c ( 29 ( 29 ( 29 ( 29 517 . 448 08 . 1 70 08 . 1 100 08 . 1 80 08 . 1 50 80 4 3 2 1 = + + + + = F ( 29 8666 . 5 5 , 08 . , / 2 = = c A F c F 45 . 76 $ 8666 . 5 517 . 448 = = c
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4    © M Pore  -  7.01  -  econ 2.ppt Exercise your understanding 0 2 1 3 4 5 years $70 $100 $80 $50 $80 0 2 1 3 4 5 years c c c c c 00 . 380 $ 70 100 80 50 80 = + + + + = F 25 . 382 $ 45 . 76 $ 5 5 = = c Which is better?
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5    © M Pore  -  7.01  -  econ 2.ppt Multiple Interest Rates $300 $500 $400 5% 6% 6% 4% 4% Find the balance at the end of year 5. 0 1 2 3 4 5 F = ?
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6    © M Pore  -  7.01  -  econ 2.ppt Solution 1: $300( / ,5%,1) $315 2: $315( / ,6%,1) $500 $833.90 3: $833.90( / ,6%,1) $883.93 4: $883.93( / ,4%,1) $400 $1,319.29 5: $1,319.29( / ,4%,1) $1,372.06 n F P n F P n F P n F P n F P = = = + = = = = + = = =
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7    © M Pore  -  7.01  -  econ 2.ppt The language of interest rates Interest rates stated without a qulifier are annual   interest rates:  9% is 9% per year. What if the compounding is not  annual? How do we ‘sync up?’ 9% per year is 9/12 = .75% per month, and .75% = .0075. 1 2 3 12 11
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8    © M Pore  -  7.01  -  econ 2.ppt Compounding monthly PV: present value FV: future value interest periods 1 2 3 12 11 F = P (1+i) 12 F = P (1+i) 12  = $100 * 1.015 12  = $119.56 r = 18% = .18 yearly rate compounded monthly  i = .18/12 = .015 monthly rate
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9    © M Pore  -  7.01  -  econ 2.ppt Taking an interest 18% = .18 is the nominal interest rate . 18% is also the  annual percentage rate (APR) . But the future value of $100  was more than $118. The future value of $100  was effectively  $ 119.56
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10    © M Pore  -  7.01  -  econ 2.ppt Taking an interest 19.56% = .1956 is the  effective interest rate .
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