Question

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 $750,000. The mortgage is currently exactly​ 18½ years​ old, and you have just made a payment. If the interest rate on the mortgage is 6.25% ​(APR), how much cash will you have from the sale once you pay off the​ mortgage? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

We calculate the principal paid off after 18.5 years (222 months) using CUMPRINC function in Excel :

rate = 6.25%/12 (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 750000 (original loan amount)

start period = 1 (We are calculating principal paid off between 1st and 222nd month)

end period = 222 (We are calculating principal paid off between 1st and 222nd month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be $296,284.287117

The balance loan principal outstanding after 18.5 years =  $750,000 - $296,284.287117 = $453,715.712883

Cash you have from the sale once you pay off the​ mortgage = sale price of house - balance loan principal outstanding

Cash you have from the sale once you pay off the​ mortgage = $1,000,000 - $453,715.712883

Cash you have from the sale once you pay off the​ mortgage = $546,284.29