Five years ago, Marcus bought a house

Computation of Initial Monthly Payment using PMT Function in Excel:

=pmt(rate,nper,-pv,fv)

Here,

PMT = Initial Monthly Payment = ?

Rate = 6%/12 = 0.50% compounded monthly 

Nper = 20 years * 12 months = 240 months

PV = $1,900,000

FV = 0

Substituting the values in formula:

=pmt(0.50%,240,-1900000,0)

PMT or Initial Monthly Payments = $13,612.19

Computation of Outstanding Principal on his Mortgage using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV =  Outstanding Principal on his Mortgage = ?

Rate = 6%/12 = 0.50% compounded monthly 

Nper = (20 years - 5 years)*12 months = 180 months

PMT = $13,612.19

FV = 0

Substituting the values in formula:

=-pv(0.50%,180,13612.19,0)

PV or  Outstanding Principal on his Mortgage = $1,613,092.36

Computation of New Monthly Payment using PMT Function in Excel:

=pmt(rate,nper,-pv,fv)

Here,

PMT = New Monthly Payment = ?

Rate = 4.5%/12 = 0.375% compounded monthly 

Nper = 15 years * 12 months = 180 months

PV = $1,613,092.36

FV = 0

Substituting the values in formula:

=pmt(0.375%,180,-1613092.36,0)

PMT or Initial Monthly Payments = $12,340.05