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["COMPUTING THE PRESENT VALUE OF A FINITE GROWING ORDINARY ANNUITY"]
["First payment, end of period, C",1000]
["Growth rate of payments, g",0.06,"Try each of the 3 scenarios!"]
["Number of future periods paid, n",5,null,null,null,{"$f":"TRANSPOSE(B10:B14)","v":1000},1060,1123.6000000000001,1191.0160000000003,1262.4769600000004]
["Discount rate, r",0.12,null,null,"!","!","!","!","!","!"]
["Present value of annuity",null,null,null,0,{"$f":"1+E6","v":1},{"$f":"1+F6","v":2},3,4,5,"Years"]
["     Using formula",{"$f":"B2*(1-((1+B3)/(1+B5))^B4)/(B5-B3)","v":4010.914471003759},{"$f":"getformula(B7)","v":"<--  =B2*(1-((1+B3)/(1+B5))^B4)/(B5-B3)"},null,"<-- Algebraic Formula: Does not work when r=g!"]
[]
["End of Period","Annuity\nPayment",null,"Payment  PV","When does the pattern of values in D10:D14 increase/decrease/stay same?"]
[1,{"$f":"B2","v":1000},{"$f":"getformula(B10)","v":"<--  =B2"},{"$f":"B10*(1+$B$5)^-A10","v":892.85714285714278},{"$f":"getformula(D10)","v":"<--  =B10*(1+$B$5)^-A10"}]
[2,{"$f":"$B$2*(1+$B$3)^(A11-1)","v":1060},{"$f":"getformula(B11)","v":"<--  =$B$2*(1+$B$3)^(A11-1)"},{"$f":"B11*(1+$B$5)^-A11","v":845.02551020408157},"<--  =B11*(1+$B$5)^-A11"]
[3,{"$f":"$B$2*(1+$B$3)^(A12-1)","v":1123.6000000000001},{"$f":"getformula(B12)","v":"<--  =$B$2*(1+$B$3)^(A12-1)"},799.7562864431485,"<--  =B12*(1+$B$5)^-A12"]
[4,{"$f":"$B$2*(1+$B$3)^(A13-1)","v":1191.0160000000003},{"$f":"getformula(B13)","v":"<--  =$B$2*(1+$B$3)^(A13-1)"},756.91219966940866,"<--  =B13*(1+$B$5)^-A13"]
[5,{"$f":"$B$2*(1+$B$3)^(A14-1)","v":1262.4769600000004},{"$f":"getformula(B14)","v":"<--  =$B$2*(1+$B$3)^(A14-1)"},716.363331829976,"<--  =B14*(1+$B$5)^-A14"]
["Sum",{"$f":"SUM(B10:B14)","v":5637.0929600000018}]
["Present value using Excel's NPV function",{"$f":"NPV(B5,B10:B14)","v":4010.9144710037572},{"$f":"getformula(B16)","v":"<--  =NPV(B5,B10:B14)"},{"$f":"SUM(D10:D14)","v":4010.9144710037581},"<--  =SUM(D10:D14)"]
[]
[]
["Equivalent value payment at end period 3",{"$f":"B10*(1+B5)^2+B11*(1+B5)+B12+B13*(1+B5)^-1+B14*(1+B5)^-2","v":5635.0460459183687},{"$f":"getformula(B19)","v":"<--  =B10*(1+B5)^2+B11*(1+B5)+B12+B13*(1+B5)^-1+B14*(1+B5)^-2"}]
["Equivalent value payment at end period 0",{"$f":"B19/(1+B5)^3","v":4010.9144710037576},{"$f":"getformula(B20)&\": Discount value at end of period 3\"","v":"<--  =B19/(1+B5)^3: Discount value at end of period 3"}]
["Equivalent value payment at end period 5",{"$f":"B20*(1+B5)^5","v":7068.6017600000023},{"$f":"getformula(B21)&\": Compound PV 5 periods\"","v":"<--  =B20*(1+B5)^5: Compound PV 5 periods"}]
[]
[null,null,"All 3 of these values are the same considering their timing!"]