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Suppose you need to get a mortgage for $500,000
Suppose you need to get a mortgage for $500,000. You would like a 17-year amortization period and plan on making quarterly payments. You find on the Internet the best mortgage rate of 4.2% (semi-annual compounding).
a) What will be the amount of your quarterly payment in that scenario?
b) How many years will it take you to pay off your mortgage if, instead of the quarterly payment amount calculated in part (a), you decide to make monthly payments of $3,200? The rest of the assumptions are the same as in part (a).
Step-by-step solution or excel with explanation.
Expert Solution
a) Computation of Amount of Quarterly Payment using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Amount of Quarterly Payment = ?
Rate = (1+4.2%/2)^2 - 1 = 4.24%/4 = 1.06%
NPER = 17 Years *4 Quarters = 68 Quarters
PV = $500,000
FV = 0
Substituting the values in formula:
=pmt(1.06%,68,-500000,0)
PMT or Amount of Quarterly Payment = $10,355.84
So, Amount of Quarterly Payment is $10,355.84.
b) Computation of Number of years It will take to Pay off the mortgage using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)/12
Here,
NPER = Number of Years It will take to pay off the Mortgage = ?
Rate = (1+4.2%/2)^2 - 1 = 4.24%/12 = 0.3537%
PMT = $3,200
PV = $500,000
FV = 0
Substituting the values in formula:
=nper(0.3537%,3200,-500000,0)/12
NPER or Number of Years It will take to pay off the Mortgage = 18.99 or 20 Years.
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