{"text_format":"1","workbook":"xlsx","n_sheets":21,"sheets":["Variables","FV Annuity End","FV Annuity End (an)","FV Annuity Begin","FV Annuity Begin (an)","PV Annuity End","PV Annuity End (an)","PV Annuity Begin","PV Annuity Begin (an)","PV Annuity End(2)","PV Annuity End(2an)","1&2","1&2 (an)","3","3 (an)","4","4 (an)","xxxx","HW ==>>","11(1)","11(2)"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":0,"defined_names":1,"comments":8,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Variables","index":0,"n_rows":16,"n_cols":3,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Financial Variable Name","Math Symbol","Excel Function Argument"]
["Present Value","PV","PV"]
["Annual Rate (APR)","i"]
["Compounding Periods per year","n"]
["Years","x"]
["Period Rate","i/n","rate"]
["Total Number of Periods","x*n","nper"]
["Periodic Payment","PMT","PMT"]
["Future Value","FV","FV"]
["Type of Annuity",null,"type"]
[]
[" >>>>>>>>","Ordinary Annuity (End)","Annuity Due (Begin)"]
[" >>>>>>>>","PMT made at end of period","PMT made at begin of period"]
[" Put into type argument for Excel Financial Functions >>>","0 or omitted",1]
[]
["Interest","FV - PV","FV - PV"]

{"sheet":"FV Annuity End","index":1,"n_rows":21,"n_cols":4,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Periodic Payment","PMT",50,"PMT"]
["Years","x",50]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",null,"rate"]
["Total Periods","x*n",null,"nper"]
["Payment at end of each month","type","omitted"]
["Future Value","FV = $ at Retirement",null," =FV(rate , nper , -PMT)"]
[]
[null,"Check:",{"$f":"C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)","v":2959811.8152382821},{"$f":"ShowFormula","v":" =C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)"}]
[]
["Future Value","FV",1000000]
["Years","x",35]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",null,"rate"]
["Total Periods","x*n",null,"nper"]
["Payment at end of each month","type","omitted"]
["Periodic Payment","PMT = Deposit $ to get $1m at Retirement",null," =PMT(rate , nper , , FV)"]
[]
[null,"Check:",{"$f":"C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))","v":118.59808915589403},{"$f":"ShowFormula","v":" =C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))"}]

{"sheet":"FV Annuity End (an)","index":2,"n_rows":21,"n_cols":4,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Periodic Payment","PMT",50,"PMT"]
["Years","x",50]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.08]
["Period Rate","i/n",{"$f":"C4/C3","v":6.6666666666666671E-3},"rate"]
["Total Periods","x*n",{"$f":"C2*C3","v":600},"nper"]
["Payment at end of each month","type","omitted"]
["Future Value","FV = $ at Retirement",{"$f":"FV(C5,C6,-C1)","v":396586.37383992266}," =FV(rate , nper , -PMT)"]
[null,"Total Amount",{"$f":"C1*C6","v":30000}]
[null,"Check:",{"$f":"C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)","v":396586.37383992266},{"$f":"ShowFormula","v":" =C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)"}]
[]
["Future Value","FV",1000000]
["Years","x",35]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",{"$f":"C15/C14","v":1.0833333333333334E-2},"rate"]
["Total Periods","x*n",{"$f":"C13*C14","v":420},"nper"]
["Payment at end of each month","type","omitted"]
["Periodic Payment","PMT = Deposit $ to get $1m at Retirement",{"$f":"PMT(C16,C17,,C12)","v":-118.59808915589218}," =PMT(rate , nper , , FV)"]
[]
[null,"Check:",{"$f":"C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))","v":118.59808915589403},{"$f":"ShowFormula","v":" =C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))"}]

{"sheet":"FV Annuity Begin","index":3,"n_rows":21,"n_cols":4,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Periodic Payment","PMT",50,"PMT"]
["Years","Years",50]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",null,"rate"]
["Total Periods","x*n",null,"nper"]
["Payment at beginning of each month","type",1]
["Future Value","FV = $ at Retirement",null," =FV(rate , nper , -PMT , , 1)"]
[]
[null,"Check:",{"$f":"C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)*(1+C4/C3)","v":2991876.4432366965},{"$f":"ShowFormula","v":" =C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)*(1+C4/C3)"}]
[]
["Future Value","FV",1000000]
["Years","Years",35]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",null,"rate"]
["Total Periods","x*n",null,"nper"]
["Payment at beginning of each month","type",1]
["Periodic Payment","PMT = Deposit $ to get $1m at Retirement",null," =PMT(rate , nper , , FV , 1)"]
[]
[null,"Check:",{"$f":"C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))/(1+C15/C14)","v":117.3270461558721},{"$f":"ShowFormula","v":" =C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))/(1+C15/C14)"}]

{"sheet":"FV Annuity Begin (an)","index":4,"n_rows":21,"n_cols":4,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Periodic Payment","PMT",50,"PMT"]
["Years","Years",50]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.08]
["Period Rate","i/n",{"$f":"C4/C3","v":6.6666666666666671E-3},"rate"]
["Total Periods","x*n",{"$f":"C2*C3","v":600},"nper"]
["Payment at beginning of each month","type",1]
["Future Value","FV = $ at Retirement",{"$f":"FV(C5,C6,-C1,,1)","v":399230.2829988554}," =FV(rate , nper , -PMT , , 1)"]
[]
[null,"Check:",{"$f":"C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)*(1+C4/C3)","v":399230.28299885546},{"$f":"ShowFormula","v":" =C1*((1+C4/C3)^(C2*C3)-1)/(C4/C3)*(1+C4/C3)"}]
[]
["Future Value","FV",1000000]
["Years","Years",35]
["# Compounding Periods per Year","n",12]
["Annual Interest Rate","i",0.13]
["Period Rate","i/n",{"$f":"C15/C14","v":1.0833333333333334E-2},"rate"]
["Total Periods","x*n",{"$f":"C13*C14","v":420},"nper"]
["Payment at beginning of each month","type",1]
["Periodic Payment","PMT = Deposit $ to get $1m at Retirement",{"$f":"PMT(C16,C17,,C12,1)","v":-117.32704615587025}," =PMT(rate , nper , , FV , 1)"]
[]
[null,"Check:",{"$f":"C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))/(1+C15/C14)","v":117.3270461558721},{"$f":"ShowFormula","v":" =C12/(((1+C15/C14)^(C13*C14)-1)/(C15/C14))/(1+C15/C14)"}]

{"sheet":"PV Annuity End","index":5,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Loan","PV",190000,"PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out)\n"]
["Annual Rate","i",4.19E-2]
["Years","x",15]
["Periods per Year","n",12]
["Period Rate","i/n"]
["Total Periods","x*n"]
["Payment at end of each month","type","ommitted"]
["Period Payment (negative cuz you pay out)","PMT = Loan Payment",null," =PMT(rate , nper , PV)"]
[]
[null,"Check:",{"$f":"C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))","v":-1423.5661203491427},{"$f":"ShowFormula","v":" =C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))"}]
[]
["Period Payment (positive cuz cash coming into business)","PMT = Cash in From Asset",10000]
["Annual Rate","i",0.15]
["Years","x",15]
["Periods per Year","n",1]
["Period Rate","i/n"]
["Total Periods","x*n"]
["Payment at end of each month","type","ommitted",null,"PV negative because it says how much cash you should pay out"]
["How much you should pay for asset","PV = Max Amount To Pay for Asset",null," =PV(rate , nper , PMT)"]
[]
[null,"Check:",{"$f":"C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)","v":-58473.700986310898},{"$f":"ShowFormula","v":" =C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)"}]

{"sheet":"PV Annuity End (an)","index":6,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Loan","PV",190000,"PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out)\n"]
["Annual Rate","i",4.19E-2]
["Years","x",15]
["Periods per Year","n",12]
["Period Rate","i/n",{"$f":"C2/C4","v":3.4916666666666668E-3}]
["Total Periods","x*n",{"$f":"C3*C4","v":180}]
["Payment at end of each month","type","ommitted"]
["Period Payment (negative cuz you pay out)","PMT = Loan Payment",{"$f":"PMT(C5,C6,C1)","v":-1423.5661203491495}," =PMT(rate , nper , PV)"]
[]
[null,"Check:",{"$f":"C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))","v":-1423.5661203491427},{"$f":"ShowFormula","v":" =C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))"}]
[]
["Period Payment (positive cuz cash coming into business)","PMT = Cash in From Asset",10000]
["Annual Rate","i",0.15]
["Years","x",15]
["Periods per Year","n",1]
["Period Rate","i/n",{"$f":"C13/C15","v":0.15}]
["Total Periods","x*n",15]
["Payment at end of each month","type","ommitted",null,"PV negative because it says how much cash you should pay out"]
["How much you should pay for asset","PV = Max Amount To Pay for Asset",{"$f":"PV(C16,C17,C12)","v":-58473.700986310905}," =PV(rate , nper , PMT)"]
[]
[null,"Check:",{"$f":"C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)","v":-58473.700986310898},{"$f":"ShowFormula","v":" =C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)"}]

{"sheet":"PV Annuity Begin","index":7,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Loan","PV",190000,"PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out)\n"]
["Annual Rate","i",4.19E-2]
["Years","x",15]
["Periods per Year","n",12]
["Period Rate","i/n",{"$f":"C2/C4","v":3.4916666666666668E-3}]
["Total Periods","x*n",{"$f":"C3*C4","v":180}]
["Payment at end of each month","type",1]
["Period Payment (negative cuz you pay out)","PMT = Loan Payment",null," =PMT(rate , nper , PV , ,1) "]
[]
[null,"Check:",{"$f":"C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))/(1+C2/C4)","v":-1418.6127973317925},{"$f":"ShowFormula","v":" =C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))/(1+C2/C4)"}]
[]
["Period Payment (positive cuz cash coming into business)","PMT = Cash in From Asset",10000]
["Annual Rate","i",0.15]
["Years","x",15]
["Periods per Year","n",1]
["Period Rate","i/n",{"$f":"C13/C15","v":0.15}]
["Total Periods","x*n",{"$f":"C14*C15","v":15}]
["Payment at end of each month","type",1,null,"PV negative because it says how much cash you should pay out"]
["How much you should pay for asset","PV = Max Amount To Pay for Asset",null," =PV(rate , nper , PMT, ,1) "]
[]
[null,"Check:",{"$f":"C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)*(1+C13/C15)","v":-67244.756134257521},{"$f":"ShowFormula","v":" =C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)*(1+C13/C15)"}]

{"sheet":"PV Annuity Begin (an)","index":8,"n_rows":21,"n_cols":5,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["Loan","PV",190000,"PV positive cuz bank lends it to you (regardless of whether you immediately pay the loan $ out)\n"]
["Annual Rate","i",4.19E-2]
["Years","x",15]
["Periods per Year","n",12]
["Period Rate","i/n",{"$f":"C2/C4","v":3.4916666666666668E-3}]
["Total Periods","x*n",{"$f":"C3*C4","v":180}]
["Payment at end of each month","type",1]
["Period Payment (negative cuz you pay out)","PMT = Loan Payment",{"$f":"PMT(C5,C6,C1,,C7)","v":-1418.6127973317991}," =PMT(rate , nper , PV , ,1) "]
[]
[null,"Check:",{"$f":"C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))/(1+C2/C4)","v":-1418.6127973317925},{"$f":"ShowFormula","v":" =C1/(((1+C2/C4)^-(C3*C4)-1)/(C2/C4))/(1+C2/C4)"}]
[]
["Period Payment (positive cuz cash coming into business)","PMT = Cash in From Asset",10000]
["Annual Rate","i",0.15]
["Years","x",15]
["Periods per Year","n",1]
["Period Rate","i/n",{"$f":"C13/C15","v":0.15}]
["Total Periods","x*n",15]
["Payment at end of each month","type",1,null,"PV negative because it says how much cash you should pay out"]
["How much you should pay for asset","PV = Max Amount To Pay for Asset",{"$f":"PV(C16,C17,C12,,C18)","v":-67244.756134257535}," =PV(rate , nper , PMT, ,1) "]
[]
[null,"Check:",{"$f":"C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)*(1+C13/C15)","v":-67244.756134257521},{"$f":"ShowFormula","v":" =C12*((1+C13/C15)^-(C14*C15)-1)/(C13/C15)*(1+C13/C15)"}]

{"sheet":"PV Annuity End(2)","index":9,"n_rows":9,"n_cols":3,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["PV = Amount in Bank on Day You Retire",395000,"PV"]
["Annual Rate",0.05,"i"]
["Years Until Money Runs Out",40,"x"]
["Periods per Year",12,"n"]
["Period Rate",null,"i/n"]
["Total Periods",null,"x*n"]
["PMT + amount you receive end each month",null," =PMT(rate,nper,-PV), cuz you deposit in bank"]
["Total Withdrawn",null,"x*n*PMT"]
["Interest",null,"Total Withdrawn - PV"]

{"sheet":"PV Annuity End(2an)","index":10,"n_rows":9,"n_cols":3,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["PV = Amount in Bank on Day You Retire",395000,"PV"]
["Annual Rate",0.05,"i"]
["Years Until Money Runs Out",40,"x"]
["Periods per Year",12,"n"]
["Period Rate",{"$f":"B2/B4","v":4.1666666666666666E-3},"i/n"]
["Total Periods",{"$f":"B3*B4","v":480},"x*n"]
["PMT + amount you receive end each month",{"$f":"PMT(B5,B6,-B1)","v":1904.6765722892724}," =PMT(rate,nper,-PV), cuz you deposit in bank"]
["Total Withdrawn",{"$f":"B7*B6","v":914244.75469885068},"x*n*PMT"]
["Interest",{"$f":"B8-B1","v":519244.75469885068},"Total Withdrawn - PV"]

{"sheet":"1&2","index":11,"n_rows":15,"n_cols":5,"rows_kept":15,"cut":false,"hidden":true,"merged":[]}
["Present Value","PV",-1000]
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",4]
["Period Rate","i/n"]
["Total Periods","n*x",null,null,"Check"]
["Future Value","FV"]
[]
["Future Value","FV",1477.4554437890627]
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",4]
["Period Rate","i/n"]
["Total Periods","n*x",null,null,"Check"]
["Present Value","PV"]

{"sheet":"1&2 (an)","index":12,"n_rows":15,"n_cols":5,"rows_kept":15,"cut":false,"hidden":true,"merged":[]}
["Present Value","PV",-1000]
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",4]
["Period Rate","i/n",{"$f":"C2/C3","v":0.05}]
["Total Periods","n*x",{"$f":"C3*C4","v":8},null,"Check"]
["Future Value","FV",{"$f":"FV(C5,C6,,C1)","v":1477.4554437890627},null,{"$f":"C1*(1+C5)^C6","v":-1477.4554437890627}]
[]
["Future Value","FV",1477.4554437890627]
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",4]
["Period Rate","i/n",{"$f":"C10/C11","v":0.05}]
["Total Periods","n*x",{"$f":"C11*C12","v":8},null,"Check"]
["Present Value","PV",{"$f":"PV(C13,C14,,C9)","v":-1000},null,{"$f":"C9/(1+C13)^C14","v":1000}]

{"sheet":"3","index":13,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":true,"merged":[]}
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",5]
["Period Rate","i/n"]
["Total Periods","n*x"]
["Future Value","FV"]
[]
["Time","Periods Remaining","Cash Flow (Individual PV amount)","Individual FV of each amount",null,"Check"]
["Time 0",10,-1000]
["Time 1",9,0]
["Time 2",8,0]
["Time 3",7,0]
["Time 4",6,-2000]
["Time 5",5,0]
["Time 6",4,-6000]
["Time 7",3,0]
["Time 8",2,0]
["Time 9",1,0]
["Time 10",0,0]
[null,null,null,null,null,null,null,null,null,"Check"]
[]
[null,null,"You can put the zeros or not"]

{"sheet":"3 (an)","index":14,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":true,"merged":[]}
["Annual Interest Rate","i",0.1]
["Number of Compounding periods per year","n",2]
["Years","x",5]
["Period Rate","i/n",{"$f":"C1/C2","v":0.05}]
["Total Periods","n*x",{"$f":"C3*C2","v":10}]
["Future Value","FV",{"$f":"SUM(D9:D19)","v":11602.123408027441}]
[]
["Time","Periods Remaining","Cash Flow (Individual PV amount)","Individual FV of each amount",null,"Check"]
["Time 0",10,-1000,{"$f":"FV($C$4,B9,,C9)","v":1628.8946267774415},null,{"$f":"(1+$C$4)^B9*-C9","v":1628.8946267774415}]
["Time 1",9,0,{"$f":"FV($C$4,B10,,C10)","v":0},null,0]
["Time 2",8,0,0,null,0]
["Time 3",7,0,0,null,0]
["Time 4",6,-2000,2680.19128125,null,2680.19128125]
["Time 5",5,0,0,null,0]
["Time 6",4,-6000,7293.0375000000004,null,7293.0375000000004]
["Time 7",3,0,0,null,0]
["Time 8",2,0,0,null,0]
["Time 9",1,0,0,null,0]
["Time 10",0,0,0,null,0]
[null,null,null,null,null,null,null,null,null,"Check"]
[null,null,null,null,null,{"$f":"SUM(F9:F19)","v":11602.123408027441},null,null,null,{"$f":"SUMPRODUCT((NPV(C4,-C10:C19)-C9)*(1+C4)^C5)","v":11602.123408027441}]
[null,null,"You can put the zeros or not"]

{"sheet":"4","index":15,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":true,"merged":[]}
["Annual Interest Rate","i",0.1,"Discount Rate"]
["Number of Compounding periods per year","n",2]
["Years","x",5]
["Period Rate","i/n"]
["Total Periods","n*x",null,null,null,null,null,null,null,"Check:"]
["Future Value","PV"]
[]
["Time","Periods","Cash Flow (Individual FV amount)","Individual PV of each amount",null,"Check"]
["Time 0",0]
["Time 1",1]
["Time 2",2]
["Time 3",3]
["Time 4",4,1000]
["Time 5",5]
["Time 6",6,2000]
["Time 7",7]
["Time 8",8]
["Time 9",9]
["Time 10",10,6000]
[]
[]
[null,null,"You can put the zeros or not"]

{"sheet":"4 (an)","index":16,"n_rows":22,"n_cols":10,"rows_kept":22,"cut":false,"hidden":true,"merged":[]}
["Annual Interest Rate","i",0.1,"Discount Rate"]
["Number of Compounding periods per year","n",2]
["Years","x",5]
["Period Rate","i/n",{"$f":"C1/C2","v":0.05}]
["Total Periods","n*x",{"$f":"C3*C2","v":10},null,null,null,null,null,null,"Check:"]
["Future Value","PV",{"$f":"SUM(D9:D19)","v":-5998.6127893096937},null,null,null,null,null,null,{"$f":"SUMPRODUCT(NPV(C4,-C10:C19))","v":-5998.6127893096909}]
[]
["Time","Periods","Cash Flow (Individual FV amount)","Individual PV of each amount",null,"Check"]
["Time 0",0,null,{"$f":"PV($C$4,B9,,C9)","v":0},null,{"$f":"-C9/(1+$C$4)^B9","v":0}]
["Time 1",1,null,{"$f":"PV($C$4,B10,,C10)","v":0},null,{"$f":"-C10/(1+$C$4)^B10","v":0}]
["Time 2",2,null,0,null,0]
["Time 3",3,null,0,null,0]
["Time 4",4,1000,-822.70247479188197,null,-822.70247479188197]
["Time 5",5,null,0,null,0]
["Time 6",6,2000,-1492.4307932732554,null,-1492.4307932732554]
["Time 7",7,null,0,null,0]
["Time 8",8,null,0,null,0]
["Time 9",9,null,0,null,0]
["Time 10",10,6000,-3683.4795212445561,null,-3683.4795212445561]
[]
[null,null,null,null,null,{"$f":"SUM(F9:F19)","v":-5998.6127893096937}]
[null,null,"You can put the zeros or not"]

{"sheet":"xxxx","index":17,"n_rows":18,"n_cols":10,"rows_kept":18,"cut":false,"hidden":true,"merged":[]}
["Cash Flows and the NPV function"]
["Interest Rate = Discount Rate = i = APR =",0.08]
["n =",1]
[]
["Method 1",null,null,null,null,"Method 2"]
["Time","Cash Flow (out (+) and in (-) of wallet)","Periods Left","PV",null,"Cash Flows for NPV are 1) Into Investment is +, 2) Out of Investment is -",null,"NPV",null,"Key is to not include Time 0 value. From Excel: \"Value1, value2, ... must be equally spaced in time and occur at the end of each period.\" Also: Cash Flows are Opposite to other Financial Functions. If you want to include time 0 value, you must adding back in at the end. Think of it as into the investment is + and out of the investment is -."]
[0,-2000,0,{"$f":"PV($B$2,C7,,B7)","v":2000},null,{"$f":"-B7","v":2000},null,{"$f":"NPV(B2,F8:F16)+F7","v":629.52996454378012}]
[1,null,1,0,null,0]
[2,-2000,2,1714.6776406035665,null,2000]
[3,1000,3,-793.83224102016959,null,-1000]
[4,1000,4,-735.02985279645327,null,-1000]
[5,-2000,5,1361.166394067506,null,2000]
[6,null,6,0,null,0]
[7,5000,7,-2917.4519763106691,null,-5000]
[8,null,8,0,null,0]
["Totals",null,"PV",{"$f":"SUM(D7:D15)","v":629.52996454378081}]
[]
[null,null,-1]

{"sheet":"HW ==>>","index":18,"n_rows":2,"n_cols":2,"rows_kept":2,"cut":false,"hidden":false,"merged":[]}
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[11.2,{"$f":"'11(2)'!A3&\", \"&'11(2)'!A4&\", \"&'11(2)'!A5&\", \"&'11(2)'!A6&\", \"&'11(2)'!A7&\", \"&'11(2)'!A8","v":"1, 2, 3, 4, 5, 6"}]

{"sheet":"11(1)","index":19,"n_rows":13,"n_cols":11,"rows_kept":13,"cut":false,"hidden":false,"merged":[]}
[null,"Perodic Payment","Number Compouning Peirods per Year","Annual Rate","Years","End or Beg?","Period Rate","Total Periods","Future Value","Total Paid","Interest"]
[null,"PMT","n","i","x","type","i/n","x*n","FV","PMT*n*x","FV - PV"]
[3,7500,2,0.06,10,0,{"$f":"D3/C3","v":0.03},{"$f":"E3*C3","v":20},{"$f":"ROUND(FV(G3,H3,-B3,,F3),2)","v":201527.81},{"$f":"ROUND(B3*C3*E3,2)","v":150000},{"$f":"I3-J3","v":51527.81}]
[4,9200,2,0.08,5,0,0.04,10,{"$f":"ROUND(FV(G4,H4,-B4,,F4),2)","v":110456.19},{"$f":"ROUND(B4*C4*E4,2)","v":92000},18456.190000000002]
[5,3500,4,0.1,7,0,2.5000000000000001E-2,28,139509.29999999999,98000,41509.299999999988]
[6,6900,4,0.04,4,0,0.01,16,119079.26,110400,8679.2599999999948]
[]
[null,"Perodic Payment","Number Compouning Peirods per Year","Annual Rate","Years","End or Beg?","Period Rate","Total Periods","Future Value","Total Paid","Interest"]
[null,"PMT","n","i","x","type","i/n","x*n","FV","PMT*n*x","FV - PV"]
[9,9500,2,0.04,9,1,{"$f":"D10/C10","v":0.02},{"$f":"E10*C10","v":18},{"$f":"ROUND(FV(G10,H10,-B10,,F10),2)","v":207485.31},{"$f":"ROUND(B10*C10*E10,2)","v":171000},{"$f":"I10-J10","v":36485.31}]
[10,1800,2,0.05,6,1,2.5000000000000001E-2,12,{"$f":"ROUND(FV(G11,H11,-B11,,F11),2)","v":25452.799999999999},{"$f":"ROUND(B11*C11*E11,2)","v":21600},3852.7999999999993]
[11,3800,4,0.08,3,1,0.02,12,51985.26,45600,6385.260000000002]
[12,10200,4,0.1,5,1,2.5000000000000001E-2,20,267069.40000000002,204000,63069.400000000023]

{"sheet":"11(2)","index":20,"n_rows":8,"n_cols":9,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
[null,"Perodic Payment","Number Compouning Peirods per Year","Years","Annual Rate","End or Beg?","Period Rate","Total Periods","Present Value"]
[null,"PMT","n","x","i","type","i/n","x*n","PV"]
[1,1800,1,18,0.1,0,{"$f":"E3/C3","v":0.1},{"$f":"D3*C3","v":18},{"$f":"ROUND(PV(G3,H3,-B3,,F3),2)","v":14762.54}]
[2,4100,1,7,0.06,0,0.06,7,{"$f":"ROUND(PV(G4,H4,-B4,,F4),2)","v":22887.759999999998}]
[3,2000,2,12,0.08,0,0.04,24,30493.93]
[4,17000,2,14,0.05,0,2.5000000000000001E-2,28,339403.11]
[5,894,4,6,0.04,0,0.01,24,18991.59]
[6,7500,4,5,0.1,0,2.5000000000000001E-2,20,116918.72]