7.01_econ_0+b - Interest Formulas Equal Payment Series 1 M...

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1   M Pore  -  7.01  -  econ 0+B.ppt Interest Formulas –  Equal Payment Series
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Equal Payment Series N F N
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3   M Pore  -  7.01  -  econ 0+B.ppt Equal Payment Series –  Compound Amount Factor 0 1 2 N 0 1 2 N A A A F 0 1 2 N A A A F =
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Process of Finding the  Equivalent Future Worth,  F 1 2 N F A (1+ i ) N -1 A (1+ i ) N -2 1 2 (1 ) 1 (1 ) (1 ) N N N i F A i A i A A i - - + - = + + + + + = L A
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5   M Pore  -  7.01  -  econ 0+B.ppt Another Way to Look at  the Compound Amount Factor
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6   M Pore  -  7.01  -  econ 0+B.ppt F A i i A F A i N N = + - = ( ) ( / , , ) 1 1 Equal Payment Series Compound Amount Factor  (Future Value of an Annuity) Example : Given:  A  = $5,000,  N  = 5 years, and  = 6% Find:  F Solution:  F  = $5,000( F/A ,6%,5) =  $28,185.46 0 1 2 3 N F A
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7   M Pore  -  7.01  -  econ 0+B.ppt Validation F =? 0 1 2 3 4 5 $5,000 $5,000 $5,000 $5,000 $5,000 i = 6% 4 3 2 1 0 $5,000(1 0.06) $6,312.38 $5,000(1 0.06) $5,955.08 $5,000(1 0.06) $5,618.00 $5,000(1 0.06) $5,300.00 $5,000(1 0.06) $5,000.00 $28.185.46 + = + = + = + = + =
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8   M Pore  -  7.01  -  econ 0+B.ppt A F i i F A F i N N = + - = ( ) ( / , , ) 1 1 Finding an Annuity Value Example : Given:  F  = $5,000,  N  = 5 years, and  = 7% Find:  A Solution:  A  = $5,000( A/F ,7%,5) =  $869.50 0 1 2 3 N F A = ?
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9   M Pore  -  7.01  -  econ 0+B.ppt Handling Time Shifts  in a Uniform Series F = ? 0 1 2 3 4 5 $5,000 $5,000 $5,000 $5,000 $5,000 i = 6% First deposit occurs at n = 0
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10   M Pore  -  7.01  -  econ 0+B.ppt 5 $5,000( / ,6%,5)(1.06) $29,876.59 F F A = = Annuity Due Excel Solution =FV(6%,5,5000,0,1) Beginning period
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11   M Pore  -  7.01  -  econ 0+B.ppt Sinking Fund Factor Example: College Savings Plan Given:  F  = $100,000,  N  = 8 years, and  = 7% Find:  A Solution:  A  = $100,000( A/F ,7%,8) =  $9,746.78 0 1 2 3 N F A ( 29 ( 29 N i F A F i i F A N , , / 1 1 = - + =
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12   M Pore  -  7.01  -  econ 0+B.ppt 0 1 2 3 4 5 6 7 8 $100,000 i = 8% A = ? Current age: 10 years old Excel Solution Given : F  =  $100,000 i  = 7% N  = 8 years  Find: =PMT( i , N ,pv,fv,type) =PMT(7%,8,0,100000,0) =$9,746.78
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13   M Pore  -  7.01  -  econ 0+B.ppt Example 3.15 Combination of a Uniform Series and a Single Present and Future Amount
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14   M Pore  -  7.01  -  econ 0+B.ppt Solution: A Two-Step Approach Step 1 : Find the required  savings at  n  = 5. Step 2 : Find the required  annual contribution ( A over 5 years. $4,298.70( / ,7%,5) $747.55 A A F = = Required Savings $500( / ,7%,5) $701.30 $5,000 $701.30 $4,298.70 C F F P F = = = - =
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15   M Pore  -  7.01  -  econ 0+B.ppt Comparison of Three Different Investment  Plans – Example 3.16
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16   M Pore  -  7.01  -  econ 0+B.ppt Solution Investor A: Investor B: Investor C: Balance at the end of 10 years 65 $33,845 $2,000( / ,9.38%,10)(1.0938)( / ,9.38%,31) $545,216 F F A F P = = 6 4 4 4 4 447 4 4 4 4 4 48 1 4 4 4 4 442 4 4 4 4 4 43 65 $322,159 $2,000( / ,9.38%,31)(1.0938) $352,377 F F P = = 1 4 4 442 4 4 4 43 65 $820,620 / ,9.38%,41)(1.0938) $897,594 F F P = = 1 4 4 442 4 4 4 43
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17   M Pore  -  7.01  -  econ 0+B.ppt How Long Would It Take  to Save $1 Million?
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18   M Pore  -  7.01  -  econ 0+B.ppt Loan Cash Flows
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19   M Pore  -  7.01  -  econ 0+B.ppt
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This note was uploaded on 03/19/2008 for the course EE 366 taught by Professor Pore during the Spring '08 term at University of Texas at Austin.

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7.01_econ_0+b - Interest Formulas Equal Payment Series 1 M...

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