Question

You have just negotiated a 5 year mortgage on $100,000 amortized over 25 years at a rate of 5%. After 5 years of payments, assume that the mortgage rate remains the same, but you change your monthly payment to $1500.

If you change your payment, how many more periods will it take you to pay off the remaining loan balance?

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

100000= Cash Flow*((1-(1+ 5/1200)^(-25*12))/(5/1200))

Cash Flow = 584.59

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-100000

I/Y =5/12

N =25*12

FV = 0

CPT PMT

Using Excel

=PMT(rate,nper,pv,fv,type)

=PMT(5/(12*100),12*25,,100000,)

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

PV= 584.59*((1-(1+ 5/1200)^(-20*12))/(5/1200))

PV = 88580.18

Using Calculator: press buttons "2ND"+"FV" then assign

PMT =584.59

I/Y =5/12

N =20*12

FV = 0

CPT PV

Using Excel

=PV(rate,nper,pmt,FV,type)

=PV(5/(12*100),12*20,,PV,)

PVOrdinary Annuity = C*[(1-(1+i/(f*100))^(-n*f))/(i/(f*100))]

C = Cash flow per period

i = interest rate

n = number of payments I f = frequency of payment

88580.18= 1500*((1-(1+ 5/1200)^(-n*12))/(5/1200))

n(in years) = 5.66

Using Calculator: press buttons "2ND"+"FV" then assign

PV =-88580.18

PMT =1500

I/Y =5/12

FV = 0

CPT N

Number of years = N/12

Using Excel

=NPER(rate,pmt,pv,fv,type)/no. of payments per year

=NPER(5/(12*100),-1500,,88580.18,)/12