{"text_format":"1","workbook":"xlsx","n_sheets":8,"sheets":["Cover","Navigator","Style Guide","Model Parameters","Minimum Payment PMT","Remaining Loan Balance CUMPRINC","No of Periods to Pay Loan NPER ","Error Checks"],"not_rendered":{"charts":0,"images":1,"macros":0,"external_links":0,"defined_names":33,"comments":0,"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"}

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["Navigator"]
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[null,null,{"$f":"Client_Name","v":"SumProduct Pty Limited"}]
[null,null,{"$f":"Model_Name","v":"SP Debt to Repay Examples.xlsm"}]
[]
[]
[]
[]
[]
[]
[]
[null,null,"Primary Developer:  Liam Bastick"]
[]
[null,null,"General Cover Notes:"]
[null,null,"This workbook provides some basic examples regarding scheduled debt payments."]
[]
[]
[]
[null,null,"Any queries, please e-mail:",null,null,null,"liam.bastick@sumproduct.com"]
[null,null,"Website:",null,null,null,"www.sumproduct.com"]

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[null,null,null,null,"Error Checks:",null,{"$f":"Overall_Error_Check","v":0}]
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[null,1,"Table of Contents"]
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[null,null,null,null,null,"Cover"]
[null,null,null,null,null,"Style Guide"]
[null,null,null,null,null,"Model Parameters"]
[null,null,null,null,null,"Minimum Payment PMT"]
[null,null,null,null,null,"Remaining Loan Balance CUMPRINC"]
[null,null,null,null,null,"No of Periods to Pay Loan NPER "]
[null,null,null,null,null,"Error Checks"]

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[null,{"$f":"MAX($B$5:$B5)+1","v":1},"Formatting of Headers / Dividers"]
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[null,null,"Model Name",null,null,null,null,null,{"$f":"C11","v":"Model Name"},null,"Model Name"]
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[null,null,"Header 4",null,null,null,null,null,{"$f":"C16","v":"Header 4"},null,"Header 4"]
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[null,null,"Notes",null,null,null,null,null,{"$f":"C18","v":"Notes"},null,"Notes"]
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[null,null,"Table Heading",null,null,null,null,null,{"$f":"C20","v":"Table Heading"},null,"Table Heading"]
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[null,null,"Constraint",null,null,null,null,null,{"$f":"C29","v":"Constraint"},null,{"$f":"C29","v":"Constraint"}]
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[null,null,"Empty",null,null,null,null,null,null,null,{"$f":"C31","v":"Empty"}]
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[null,null,"Error Check",null,null,null,null,null,0,null,{"$f":"C33","v":"Error Check"}]
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[null,null,"Hyperlink",null,null,null,null,null,"Hyperlink",null,{"$f":"C35","v":"Hyperlink"}]
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[null,null,"Line Calculation",null,null,null,null,null,77,null,"Line Calc"]
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[null,null,"Line Total",null,null,null,null,null,{"$f":"I39","v":77},null,{"$f":"C41","v":"Line Total"}]
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[null,null,"Parameter",null,null,null,null,null,365,null,{"$f":"C43","v":"Parameter"}]
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[null,null,"Range Name Description",null,null,null,null,null,"Not_Named",null,{"$f":"C45","v":"Range Name Description"}]
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[null,null,"Row Reference",null,null,null,null,null,{"$f":"ROW(C47)","v":47},null,"Row Ref"]
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[null,null,"Row Summary",null,null,null,null,null,{"$f":"I41","v":77},null,{"$f":"C49","v":"Row Summary"}]
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[null,null,"Units",null,null,null,null,null,"A$",null,{"$f":"C51","v":"Units"}]
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[null,{"$f":"MAX($B$5:$B5)+1","v":1},"General"]
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[null,null,"Key Inputs"]
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[null,null,null,null,"General"]
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[null,{"$f":"MAX($B$5:$B14)+1","v":2},"General Range Names"]
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[null,null,"Technical Assumptions"]
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[null,null,null,null,"Days in Year",null,365]
[null,null,null,null,"Months in Month",null,1]
[null,null,null,null,"Months in Quarter",null,3]
[null,null,null,null,"Months in Half Yr",null,6]
[null,null,null,null,"Months in Year",null,12]
[null,null,null,null,"Quarters in Year",null,4]
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[null,null,null,null,"Rounding Accuracy",null,5]
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[null,null,null,null,"Very Large Number",null,9.9999999999999997E+98]
[null,null,null,null,"Very Small Number",null,1E-8]
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[null,null,null,null,"Thousand",null,1000]

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["Navigator"]
[null,null,null,null,"Error Checks:",null,null,null,{"$f":"Overall_Error_Check","v":0}]
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[null,{"$f":"MAX($B$5:$B5)+1","v":1},{"$f":"A1","v":"Minimum Payment PMT"}]
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[null,null,"Payments in Arrears"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Imagine you borrow an amount A to be repaid over N periods with a periodic interest rate of i."]
[null,null,null,null,null,"Assuming payments are made at the end of each period, the amount to be paid each period will be P:"]
[]
[null,null,null,null,null,null,"P = Ai / (1 - (1 + i)^-N)"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how it works:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Repayment Period (Years)",null,null,null,25]
[null,null,null,null,null,null,"Repayment Period (Months) (N)",null,null,null,{"$f":"K23*Months_in_Year","v":300}]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K25/Months_in_Year","v":5.0000000000000001E-3}]
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[null,null,null,null,null,null,"Monthly Payment",null,null,null,{"$f":"(K22*K26)/(1-((1+K26)^-K24))","v":1932.904204456551}]
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[null,null,null,null,null,null,"PMT Calculation",null,null,null,{"$f":"-PMT(K26,K24,K22)","v":1932.9042044565256}]
[]
[]
[null,null,"Payments in Advance"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Again, assume you borrow an amount A to be repaid over N periods with a periodic interest rate of i."]
[null,null,null,null,null,"With payments made at the beginning of each period, the amount to be paid each period will be P:"]
[]
[null,null,null,null,null,null,"P = Ai / ((1 - (1 + i)^-N) * (1 + i))"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how it works:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Repayment Period (Years)",null,null,null,25]
[null,null,null,null,null,null,"Repayment Period (Months) (N)",null,null,null,{"$f":"K48*Months_in_Year","v":300}]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K50/Months_in_Year","v":5.0000000000000001E-3}]
[]
[null,null,null,null,null,null,"Monthly Payment",null,null,null,{"$f":"(K47*K51)/((1-((1+K51)^-K49))*(1+K51))","v":1923.2877656284093}]
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[null,null,null,null,null,null,"PMT Calculation",null,null,null,{"$f":"-PMT(K51,K49,K47,,1)","v":1923.2877656283836}]

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[null,null,null,null,"Error Checks:",null,null,null,{"$f":"Overall_Error_Check","v":0}]
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[null,{"$f":"MAX($B$5:$B5)+1","v":1},{"$f":"A1","v":"Remaining Loan Balance CUMPRINC"}]
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[null,null,"Payments in Arrears"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Imagine you borrow an amount A to be repaid over N periods with a periodic interest rate of i."]
[null,null,null,null,null,"Assuming payments are made at the end of each period, the remaining loan balance B after n periods (n <= N) will be:"]
[]
[null,null,null,null,null,null,"B = A (1 + i)^n - ((P / i) [(1 + i)^n - 1])"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how to calculate it:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Repayment Period (Years)",null,null,null,25]
[null,null,null,null,null,null,"Repayment Period (Months) (N)",null,null,null,{"$f":"K23*Months_in_Year","v":300}]
[null,null,null,null,null,null,"Month Number (n <= N)",null,null,null,36]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K26/Months_in_Year","v":5.0000000000000001E-3}]
[null,null,null,null,null,null,"Monthly Payment (P)",null,null,null,{"$f":"(K22*K27)/(1-(1+K27)^-K24)","v":1932.904204456551},{"$f":"\"using \"&'Minimum Payment PMT'!$G$15","v":"using P = Ai / (1 - (1 + i)^-N)"}]
[]
[null,null,null,null,null,null,"Outstanding Balance (B)",null,null,null,{"$f":"K22*((1+K27)^K25)-((K28/K27)*(((1+K27)^K25)-1))","v":282971.23477384471}]
[]
[null,null,null,null,null,null,"CUMPRINC Calculation",null,null,null,{"$f":"K22+CUMPRINC(K27,K24,K22,one,K25,0)","v":282971.23477384512}]
[]
[null,null,null,null,null,null,"CUMPRINC actually calculates the principal paid off between periods x and y, where y >= x."]
[null,null,null,null,null,null,"This is why the value '1' has been hardcoded into the formula above."]
[null,null,null,null,null,null,"Therefore, the balance remaining is the original amount less the principal paid off."]
[]
[null,null,null,null,null,null,"Total Interest Paid so far",null,null,null,{"$f":"K25*K28-(K22-K32)","v":52555.786134280963}]
[]
[]
[null,null,"Payments in Advance"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Again, you borrow an amount A to be repaid over N periods with a periodic interest rate of i."]
[null,null,null,null,null,"Assuming payments are made at the beginning of each period, the remaining loan balance B after n periods (n <= N) will be:"]
[]
[null,null,null,null,null,null,"B = (A - P)(1 + i)^n - ((P / i) [(1 + i)^n - (1 + i)])"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how to calculate it:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Repayment Period (Years)",null,null,null,25]
[null,null,null,null,null,null,"Repayment Period (Months) (N)",null,null,null,{"$f":"K56*Months_in_Year","v":300}]
[null,null,null,null,null,null,"Month Number (n <= N)",null,null,null,36]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K59/Months_in_Year","v":5.0000000000000001E-3}]
[null,null,null,null,null,null,"Monthly Payment (P)",null,null,null,{"$f":"(K55*K60)/((1-(1+K60)^-K57)*(1+K60))","v":1923.2877656284093},{"$f":"\"using \"&'Minimum Payment PMT'!$G$40","v":"using P = Ai / ((1 - (1 + i)^-N) * (1 + i))"}]
[]
[null,null,null,null,null,null,"Outstanding Balance (B)",null,null,null,{"$f":"(K55-K61)*((1+K60)^K58)-((K61/K60)*(((1+K60)^K58)-(1+K60)))","v":282971.23477384466},"note the balance will always be the same whether paid in arrears or in advance"]
[]
[null,null,null,null,null,null,"CUMPRINC Calculation",null,null,null,{"$f":"(K55+CUMPRINC(K60,K57,K55,one,K58,1))*(1+K60)","v":282971.23477384512},"this is multiplied by (1 + i) as interest accrues by the end of the period (the final payment is made at the beginning of the period)"]
[]
[null,null,null,null,null,null,"CUMPRINC actually calculates the principal paid off between periods x and y, where y >= x."]
[null,null,null,null,null,null,"This is why the value '1' has been hardcoded into the formula above."]
[null,null,null,null,null,null,"Therefore, the balance remaining is the original amount less the principal paid off PLUS the interest in the final period (payment is made at the start of the period)."]
[]
[null,null,null,null,null,null,"Total Interest Paid so far",null,null,null,{"$f":"K58*K61-(K55-K65)","v":52209.594336467853}]

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[null,null,null,null,"Error Checks:",null,null,null,{"$f":"Overall_Error_Check","v":0}]
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[null,{"$f":"MAX($B$5:$B5)+1","v":1},{"$f":"A1","v":"No of Periods to Pay Loan NPER "}]
[]
[null,null,"Payments in Arrears"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Imagine you borrow an amount A with an associated periodic interest rate of i."]
[null,null,null,null,null,"How many periods will it take to pay off the loan if you pay an amount P at the end of each period?"]
[]
[null,null,null,null,null,null,"N = -log(1 - (Ai / P)) / log (1 + i)",null,null,null,null,"Note: it does not matter which logarithmic base you use as long as it is the same for the numerator and the denominator"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how it works:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K23/Months_in_Year","v":5.0000000000000001E-3}]
[null,null,null,null,null,null,"Monthly Payment (P)",null,null,null,5000]
[]
[null,null,null,null,null,null,"Number of Months (N)",null,null,null,{"$f":"-LOG(1-(K22*K24/K25))/LOG(1+K24)","v":71.513178015521419},"This figure could be rounded up though if not an integer"]
[]
[null,null,null,null,null,null,"NPER Calculation",null,null,null,{"$f":"NPER(K24,-K25,K22)","v":71.513178015521419}]
[]
[]
[null,null,"Payments in Advance"]
[]
[null,null,null,"Scenario"]
[]
[null,null,null,null,null,"Again, you borrow an amount A with an associated periodic interest rate of i."]
[null,null,null,null,null,"How many periods will it take to pay off the loan if you pay an amount P at the beginning of each period?"]
[]
[null,null,null,null,null,null,"N = 1 - log(1 - ((A - P) i / P)) / log (1 + i)",null,null,null,null,"Note: it does not matter which logarithmic base you use as long as it is the same for the numerator and the denominator"]
[]
[]
[null,null,null,null,"Illustration"]
[]
[null,null,null,null,null,"This formula shows how it works:"]
[]
[null,null,null,null,null,null,"Amount (A)",null,null,null,300000]
[null,null,null,null,null,null,"Annual Interest Rate (%)",null,null,null,0.06]
[null,null,null,null,null,null,"Monthly Interest Rate (%) (i)",null,null,null,{"$f":"K47/Months_in_Year","v":5.0000000000000001E-3}]
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