1,Chapter 14 Loan Amortization;Mortgage,14.3 mortgage loans-fundamentals,2,Basic concepts and definitions,A mortgage loan is a loan secured by some physical property. The face value of the mortgage is the original principal amount that borrower promises to repay. In legal language, the borrower is called the mortgagor and the lender is called the mortgagee.,3,The term of a mortgage loan is the length of time from the date on which the loan is advanced to the date on which the remaining principal balance is due and payable.,4,Calculating the payment and the balance,Mortgage interest rates advertised by most financial institutions are semiannually compounded rates. The majority of mortgages require monthly payments.,5,The payments for the initial term are calculated as though the interest rate is fixed for the entire amortization period.,PV,PMT,n,1/y,FV,0,result,p,Original loan,n,n represents the number of payments in the amortization period.,CPT,6,The principal balance on the mortgage loan after any payment may be calculated using either the prospective method or the retrospective method. The latter is preferable.,7,The principal and interest components of any mortgage payment may be calculated as described in section 14.1 Particularly when the amortization period is 20 or 25 years, the payment in the first few years are primarily interest.,8,The Composition of Mortgage Payments during a 25-year AmortizationFigure 14.3,Principal portion,interest portion,9,A Mortgages Declining Balance During a 25-Year AmortizationFigure 14.4,10,Example,A $50,000 mortgage loan is written with a 20-year amortization period, a 3-year term, and an interest rate of 9.5% compounded semiannually. Payments are made monthly. Calculate:a, the balance at the end of the 3-year term.b, the size of the payments upon renewal for 5 years at 10.5% compounded semiannually (with the loan maintaining its original 20-year amortization),11,Solution:,j=9.5% compounded semiannually i=j/m=4.25% payment interval=1 month p=(1+i)c-1=0.776438317% An=$50,000 term of amortization=20 yearsn=12*20=240,Question a,12,Compute the payment size,PV,PMT,n,1/y,FV,0,-460.115,0.776438317,50,000,240,Payment=$460.115,PV,+/-,n,FV,-47,026.83,50,000,36,Balance after 3-yearis $47,026.83,PMT,Retrospective Method,CPT,CPT,13,j=10.5% compounded semiannually i=j/m=5.25% payment interval=1 month p=(1+i)c-1=0.856451515%the balance after 3-year is $47,026.83.The remaining payments are (20-3)*12=204,Question b,14,PV,PMT,n,1/y,FV,0,-488.533,0.856451515,47,027.51,204,The payment upon renewal for5 years at 10.5% compoundedsemiannually is $488.54.,CPT,15,Example,The monthly payments for the first 5-year term of a $20,000 mortgage loan were based on a 10-year amortization and an interest rate of 9.9% compounded semiannually. The payments were rounded up to the next higher $10.A, calculate the size of the monthly payments.B, what is the principal balance at the end of the 5-year term?C, if the interest rate at renewal is 9% compounded semiannually for a 5-year term, calculate the new monthly payments, also rounded to the next higher $10.D, calculate the size of the last payment.,16,Original loan=$20,000 term=10 yearsj=9.9% compounded semiannuallypayment interval=1 month n=10*12=120i=j/m=4.95%,Solution:,17,A, calculate the size of the monthly payments,the monthly payment rounded to the next higher $10 is $270.,PV,PMT,n,1/y,FV,0,-261.01,8.0848171,20,000,120,CPT,18,B, the principal balance at the end of the 5-year term is the principal balance after 60th payment,R=$270 original loan=$20,000 p=8.0848171% n=5*12=60,+/-,n,FV,-11,679.06,60,PMT,Retrospective Method,270,The principal balance at the end of the 5-year term is $11,679.06,CPT,19,C,calculate the new monthly payment,j=9% compounded semiannually i=4.5%the monthly payment on renewal, rounded to the next higher $10, will be $250.,PV,PMT,n,1/y,FV,0,-241.51,7.363123,11,679.06,60,CPT,20,D, calculate the size of the last payment,Principal balance after 5 years=$11,679.06 R=$250 p=7.363123%,PV,+/-,n,1/y,FV,0,57.4634123,7.363123,11,679.06,250,PMT,The exact number ofpayments is 58. The lastpayment is less than $250.,CPT,21,final payment=(1+7.363123%)*115.23 =$116.08,Final payment,=,(1+P)*,Balance after the second-to-lastpayment,n,FV,-115.23,57,Retrospective Method,PV,11,679.06,+/-,1/y,7.363123,250,PMT,CPT,22,Qualifying for a mortgage loan,Three key lending principles:,The loan should not exceed acertain fractionof the value of the propertysecuring the loan.,The payments associated withhome ownership should not exceeda certain percentage of the borrowersregular grossincome.,The payments associated withhome ownershipand all otherdebt should notexceed a certainpercentage ofthe borrowersregular grossincome.,