Question

# You have just sold your house for \$1,000,000 in cash. Your mortgage was originally a 30-year...

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 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?? Monthly payment?? Periods remaining?? PV of mortgage?? Cash from sale??

Discount Rate = APR/12 = 5.25%/12 = 0.438%

Monthly Repayment can be calculated using formula:

PV = A * [(1-((1+r)^(-n))/r]

• 800000 = A * [(1-((1+.438%)^(-360))/.438%]
• A = \$4420.61

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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