Question

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??

Answer 1

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