You have just sold your house for $1,000,000 in cash. Your mortgage was originally a 30year mortgage with monthly payments and an initial balance of $800,000. The mortgage is currently exactly 18½ 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?
Sale price  $ 1,000,000  
Initial balance  $ 800,000  
Number of years  30  
Periods per year  12  
Periods into the loan  222  
5.25% APR

Discount Rate = APR/12 = 5.25%/12 = 0.438%
Monthly Repayment can be calculated using formula:
PV = A * [(1((1+r)^(n))/r]
Hence, Monthly repayment amount is $4420.61
Period Remaining = Loan term – periods into the loan = 360 – 222 = 138
PV of mortgage at time 222 = $4420.61 * [(1((1+.438%)^(138))/.438%] = $457097.19
Cash from Sale = $1,000,000  $457,097.19 = $542,902.81
Discount Rate 
0.438% 
Monthly Repayment 
$ 4,420.61 
Period Remaining 
138 
PV of Mortgage 
$ 457,097.19 
Cash From Sale 
$ 542,902.81 
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