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Homework answers / question archive / Five years ago, Marcus bought a house
Five years ago, Marcus bought a house. He secured a mortgage from his bank for $1, 900, 000. The mortgage had monthly payments for 20 years with an interest rate of 6.0% compounded monthly. Interest rates have fallen to 4.5% compounded monthly, and Marcus still intends to make monthly payments and to pay back the debt over the remaining 15 years.
a) How much were Marcus' initial monthly payments?
b) What is the outstanding principal on his mortgage?
c) How much are Marcus' new monthly payments?
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
