6. You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30-year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 181/2 years old, and you have just made a payment. If the interest rate on the mortgage is 5.25% (APR), how much cash will you have from the sale once you pay off the mortgage? ( $543,069)

$543,069

Explanation:

The starting point of this analysis is to determine the monthly payment under the mortgage using excel pmt function as shown below:

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

rate=monthly interest rate=5.25% /12

nper=number of monthly payments in 30 years=30*12=360 months

pv=mortgage amount=-800000

fv=0(the balance after all month payments is zero)

=pmt(5.25% /12,360,-800000,0)=$4,417.63  

Number of month payments already made=18.5*12=222

Number of monthly payments outstanding=360-222=138

The balance of the mortgage now is the present of remaining mortgage payments

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

rate=5.25% /12

nper=138

pmt=4417.63

fv=0

=-pv(5.25% /12,138,4417.63,0)

pv=$456,931

Cash balance=cash proceeds from sale of house-outstanding mortgage balance

Cash balance=$1,000,000-$456,931=$543,069  

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